•Engineering 
T  ; 


of; 


USEFUL  DATA 

ON 
REINFORCED  CONCRETE  BUILDINGS 

FOR  THE 

DESIGNER  AND  ESTIMATOR 

BY  THE 

ENGINEERING  STAFF 

OF  THE 

CORRUGATED  BAR  COMPANY,  INC. 


UNIVERSITY  OF  CAUFOR1 
PARTMENT  OF  CIVIL 
PRICE,  $2S»t- 

SECOND  EDITION 


CORRUGATED  BAR  COMPANY,  INC. 

BUFFALO,  N.  Y. 
1919 


[I 


Engineering 


Copyright,  1920 

By  CORRUGATED  BAR  COMPANY,  INC. 
BUFFALO,  N.  Y. 


PREFACE 

FOR  more  than  25  years  we  have  been  engaged  in  the  design 
and  development  of  reinforced  concrete  construction.  During 
this  period  we  have  had  occasion  to  publish  technical  data 
from  time  to  time  of  interest  to  the  engineer,  the  architect  and  the 
contractor.  As  a  result  of  these  publications  we  find  there  is  a  growing 
demand  for  a  compilation  of  data  relating  to  the  design  of  reinforced 
concrete  buildings.  A  number  of  comprehensive  treatises  have  been 
published  to  meet  this  demand,  but  they  deal  generally  with  method 
and  theory  of  design  rather  than  with  quantitative  results. 

It  is  not  intended,  nor  is  it  expected,  that  this  handbook  can  take 
the  place  of  any  of  the  excellent  textbooks  on  concrete  design  or 
replace  the  services  of  the  designing  engineer.  It  is  hoped  that  it 
will  supplement  the  works  of  reference  and  as  far  as  possible  eliminate 
the  manual  labor  involved  in  the  repeated  application  of  formulas 
and  diagrams  to  the  determination  of  the  dimensions  of  a  structure. 
It  is  the  further  aim  of  the  book  to  give  under  one  cover  all  of  the 
data  needed  by  the  busy  engineer  or  estimator  in  meeting  the  every- 
day problems  in  concrete  building  design,  or  briefly  to  place  in  his 
hands  designing  information  that  in  a  measure  parallels  the  familiar 
handbook  of  the  structural  steel  manufacturer. 

Until  such  time  as  a  national  building  code  may  be  adopted, 
there  will  be  recognized  the  impossibility  of  preparing  a  thoroughly 
satisfactory  set  of  reinforced  concrete  standards  so  that  we  have  of 
necessity  confined  ourselves  to  stress  combinations  most  widely 
accepted  and  within  these  limits  to  give  a  satisfactory  range  of 
working  values, — values  that  give  the  "answer,"  without  further 
resort  to  calculation,  when  the  conditions  of  the  problem  are  known. 

Several  of  the  more  comprehensive  publications  on  reinforced  con- 
crete contain  some  excellent  diagrams  that  greatly  facilitate  the 
designer's  work.  A  few  of  these  diagrams  have  been  incorporated  in 
the  present  volume  and  due  acknowledgment  for  their  use  is  hereby 
made  to  the  work  of  Messrs.  Turneaure  & Maurer  entitled  "Principles 
of  Reinforced  Concrete  Construction"  and  to  "Reinforced  Concrete 
Construction,"  by  George  A.  Hool,  S.  B.,  Professor  of  Structural 
Engineering,  University  of  Wisconsin.  Further  acknowledgment 
is  also  made  to  those  members  of  our  organization  who  so  ably 
assisted  in  the  compilation  of  the  data  and  to  their  efforts  is  due 
what  measure  of  success  may  attend  the  publication  of  this  volume. 

CORRUGATED  BAR  COMPANY,  INC. 
Buffalo,  N.  Y.,  March  15,  1919. 

785274 


FORMULAS  FOR  REINFORCED   CONCEETTE 
DESIGIST 

It  is  recognized  by  all  authorities  on  the  -design  of  reinforced  concrete  structures, 
that  the  common  theory  of  flexure  does  not  apply  for  wide  ranges  of  stress.  For 
stresses  in  excess  of  those  commonly  used  in  design  the  relation  between  stress  and 
deformation  is  not  uniform  and  this  divergence  becomes  more  pronounced  as  the 
stress  increases.  Under  these  conditions  the  parabola  is  the  curve  which  most  nearly 
expresses  the  relation  between  stress  and  deformation  and  is  the  relation  which  should 
be  used  in  the  discussion  of  experimental  or  test  data  to  obtain  accuracy  of  results. 

In  the  design  of  structures,  however,  the  stresses  used  are  low,  a  condition  for  which 
it  can  safely  be  assumed  that  the  deformation  of  any  compression  fibre  in  a  beam  is 
proportional  to  its  distance  from  the  neutral  axis.  The  error  in  this  assumption  is 
small  and  is  on  the  side  of  safety. 

The  formulas  which  follow  are  for  working  loads  and  assume  a  straight  line  varia- 
tion of  stress  to  deformation  of  concrete  in  compression.  Tension  in  the  concrete  is 
neglected. 

*  STANDARD  NOTATION 

(a)  Rectangular  Beams. 

The  following  notation  is  recommended: 
fa  =  tensile  unit  stress  in  steel. 
/c  =compressive  unit  stress  in  concrete. 
Ea  =  modulus  of  elasticity  of  steel. 
EC  =  modulus  of  elasticity  of  concrete. 


M  =  moment  of  resistance,  or  bending  moment  in  general. 

Aa  =  steel  area. 

6    =  breadth  of  beam. 

d    =  depth  of  beam  to  center  of  steel. 

k    =  ratio  of  depth  of  neutral  axis  to  depth  d. 

z    =  depth  below  top  to  resultant  of  the  compressive  stresses. 

j     =  ratio  of  lever  arm  of  resisting  couple  to  depth  d. 

jd  =d—  z  =  arm  of  resisting  couple. 

p    =  steel  ratio  =T-J- 

(b)  T-Beams. 

b    =  width  of  flange. 

bf  =  width  of  stem. 

t     —  thickness  of  flange. 

(c)  Beams  Reinforced  for  Compression. 

A'  =area  of  compressive  steel. 

p'  =  steel  ratio  for  compressive  steel. 

/„'  =  compressive  unit  stress  in  steel. 

C   =  total  compressive  stress  in  concrete. 

*  From:     Transactions  of  Am.  Soc.  of  C.  E.  Vol.  LXXXI,  December,  1917. 


CORRUGATED   BAR   COMPANY,   INC 


C"  =  total  compressive  stress  in  steel. 
d'  =  depch  to  center  of  eompressive  steel. 
z  = depth  to  resultant  of  C  and  C'. 

(d)  Shear,  Bond  and  Web  Reinforcement. 

V  =  total  shear. 

V  =  total  shear  producing  stress  in  reinforcement. 
v    =  shearing  unit  stress. 
u    =  bond  stress  per  unit  area  of  bar. 
o    =  circumference  or  perimeter  of  bar. 
2o=sum  of  the  perimeters  of  all  bars. 
Ta  =  total  stress  in  single  reinforcing  member. 
s  =  Horizontal  spacing  of  reinforcing  members. 

(e)  Columns. 

A  =  total  net  area. 

A»  =  area  of  longitudinal  steel. 

AC  =area  of  concrete. 

P  =  total  safe  load. 

(a)  Rectangular  Beams. 

Position  of  neutral  axis, 

Arm  of  resisting  couple, 


FORMULAS 


k  =  -V2pn+  (pn)z  —  pn. 


(D 
(2) 


[For /B  =  15,000  to  16,000  and  /0  =  600  to  650,  j  may  be  taken  at  ~ 

o 


Fiber  stresses, 


M        M 


/8     A.jd 

2M  _2pfa 
Jc    jkbd*       k 


(3) 
(4) 


USEFUL      DATA 


Steel  ratio,  for  balanced  reinforcement, 

1  1 


(5) 


(6)  T-Beams. 


FIG.  2. 

Case  I.   When  the  neutral  axis  lies  in  the  flange,  use  the  formulas  for  rectan- 
gular beams. 

Case  II.   When  the  neutral  axis  lies  in  the  stem. 

The  following  formulas  neglect  the  compression  in  the  stem. 
Position  of  neutral  axis, 

ft* 


2nAa+2bt 


Position  of  resultant  compression, 


Arm  of  resisting  couple, 
Fiber  stresses, 


2kd-t      3 
jd=d—z. 


f-JL 

h     Aajd 


Mkd 


bt(kd-\t)jd 


fs         k 

n    l-k 


(6) 
(7) 
(8) 

(9) 
(10) 


(For  approximate  results  the  formulas  for  rectangular  beams  may  be  used.) 
The  following  formulas  take  into  account  the  compression  in  the  stem;   they  are 
recommended  where  the  flange  is  small  compared  with  the  stem: 
Position  of  neutral  axis, 


j2 
\ 


(b-b')t*       (nAa+(b-b')t\*      nAa+(b-b')t. 
b'  r  \          b'          )  b' 


Position  of  resultant  compression, 


(12) 


t(2kd-t)b+(kd-t)*  b' 
7 


CORRUGATED      BAR      COMPANY,      INC. 


Arm  of  resisting  couple, 
Fiber  stresses, 


/•  = 
/.= 


M 

ABjd 


2Mkd 


[(2kd-i)bt+(kd-t)*b']jd 
(c)  Beams  Reinforced  for  Compression. 


FIG.  3. 


Position  of  neutral  axis, 


')*  -n(p+p'} 


Position  of  resultant  compression, 


Arm  of  resisting  couple, 
Fiber  stresses, 

/c=- 


QM 


M          A-k 

nfe~ 


Shear,  Bond,  and  Web  Reinforcement. 

For  rectangular  beams, 


(13) 

(14) 
(15) 


(16) 

(17) 

(18) 

(19) 

(20) 
(21) 

(22) 


USEFUL      DATA 


(For  approximate  results  j  may  be  taken  at  £•) 

The  stresses  in  web  reinforcement  may  be  estimated  by  means  of  the  following 
formulas: 

Vertical  web  reinforcement, 

V'a 

T-=i£  (24> 

Bars  bent  up  at  angles  between  20  and  45  deg.  with  the  horizontal  and  web  members 
inclined  at  45  deg., 


In  the  text  of  the  report  it  is  recommended  that  two-thirds  of  the  external  vertical 
shear  (total  shear)  at  any  section  be  taken  as  the  amount  of  total  shear  producing 
stress  in  the  web  reinforcement.  V  therefore  equals  two-thirds  of  V. 

The  same  formulas  apply  to  beams  reinforced  for  compression  as  regards  shear  and 
bond  stress  for  tensile  steel. 

For  T-Beams, 

v=Vjd  (26) 

w=-  (27) 


[For  approximate  results  j  may  be  taken  at  ^  •  ] 

o 

(e)  Columns. 

Total  safe  load, 

P=/cUc+nyl8)  =fcA(l+(n-l)p]  (28) 

Unit  stresses, 

(29) 


/s=n/c  (30) 


CORRUGATED   BAR   COMPANY,  INC. 


EXPLANATION  OF  THE  USE  OF  DESIGNING 
DIAGRAMS 

Rectangular  beams  or  slabs,  reinforced  for  tension  only,  may  readily  be  designed 
by  the  aid  of  Diagram  1,  page  16.  This  diagram  assumes  a  value  for  E0  of  2,000,000 
or  n  =  15,  which  is  recommended  for  the  design  of  beams  and  slabs. 

Example  1. — Given  a  beam  having  a  span  of  24  ft.  simply  supported,  to  carry 
a  load  of  4,000  Ib.  per  ft.  including  estimated  dead  load;  /c  =  650,  fa  =  16,000,  E0= 
2,000,000,  n  =  15.  Determine  size  of  beam  required. 

u_  (4,000)(24)(24)  =288j(x)0  ft  lb  =3>456000  in  ,b 

o 

On  Diagram  1,  page  16,  find  the  intersection  of  curves  for /8  =  16.000  and /c  =  650 
and  read  K=  ^  =107.5  and  p=0.77%=0.0077 

M_  3,456,000 


A         -      A    OA-      *  M          3,456,000 

Assuming  6=24  in,  d  =  ^  =  \(24)(1Q75)  =36.6 

^=^=(0.0077X24X36.6)  =6.76  sq.  in. 

It  will  be  noted  that  by  selecting  a  value  for  either  6  or  d  the  problem  may  be  com- 
pletely solved.  This  selection  may  be  governed  by  the  relative  cost  of  steel  and  con- 
crete or  may  be  limited  by  clearance. 

Care  should  always  be  taken  to  ascertain  if  the  section  selected  to  resist  bending 
moment  is  satisfactory  in  shear.  In  the  example: 


V  48,000 

»=  TT-T  =  -  7=r  -  =  62.5  lb.  per  sq.  m. 


(24)        (36.6) 

It  will  be  noted  that  j  has  been  taken  as  3*  which  is  sufficiently  close  when  used  in 

o 

calculations  for  bond  and  shear  stresses.    The  result  indicates  web  reinforcement 
would  be  required,  for  a  limit  of  40  lb.  per  sq.  in.  shear  on  the  concrete. 

Example  2.  —  Given  a  beam  of  20  ft.  span  having  fixed  ends  and  carrying  a  total 
load  of  1,000  lb.  per  ft;  6  =  10  in.,  d=18  in,  Aa  =  2.  20  sq.  in.  and  n  =  15.  Find/6, 
/<.,  j  and  k. 


M=      400,000 
fed2     (10)  (18)  (18) 


10 


USEFUL      DATA 


On  Diagram  1  find  the  intersection  of  K=123.5  and  p=1.22  and  read  /8  =  11,900, 
fe  =  650.  On  the  upper  portion  of  the  diagram  for  p  =  1  .  22  find  j  =  0  .  846  and  k  =  0  .  452. 

T-Beams.  In  the  design  and  investigation  of  T-beams  Diagrams  2,  3  and  4,  pages 
17,  18  and  19  will  be  found  useful.  These  diagrams  apply  only  when  the  neutral  axis 
falls  below  the  under  side  of  the  flange  of  the  T-beam.  When  the  neutral  axis  falls 
above,  the  diagrams  for  rectangular  beams  apply. 

Diagram  2  can  be  used  only  when  the  area  of  steel  is  such  that/8  is  16,000  and  Dia- 
gram 3  when  /B  is  18,000.  From  these  diagrams,  for  any  assumed  value  of  d  and  for 
fixed  values  of  M  ,  t  and  b,  we  may  obtain  .;  for  determining  the  steel  area  required  and 
also  the  value  of  /c.  If  /c  is  fixed,  knowing  M  and  t,  we  may  find  the  value  of  b  or  d, 
by  assuming  one  of  them,  and  obtain  the  corresponding  steel  area.  It  should  be  borne 
in  mind  that  b  must  not  exceed  code  or  specification  limits. 

Diagram  4  gives  values  of  k  and  j  for  T-beams  and  is  useful  in  checking  steel  and 
concrete  stresses,  the  dimensions  and  reinforcement  being  known. 

Example  1.  Given  a  T-beam  having  a  span  of  24  feet,  freely  supported,  to  carry 
a  total  load  of  2,000  Ib.  per  foot,  *=5  in.,  6  =  30  in.,  /„  =  1  6,000,  /c  =  650,  n  =  15,  t?  =  120. 


4>  =24,000 


Assuming  a  width  of  stem  of  10  in.  we  find  from  shear  considerations, 

V  24000 

=22.85  m. 


t 

From  Diagram  2  trace  upward  from  the  value  of  -  =0.219  to  intersection  with  the 

a 

curve  f  or  /c  =  650  and  read  ^  =92.0.    Substituting  for  M  and   d  the   values  given 

above  we  find 

1,728,000         _ 
(6)  (22.  85)  (22.85) 
6  =  35.  8  in. 

This  exceeds  the  fixed  dimension  of  30  in.  for  6  so  that  it  becomes  necessary  to 
assume  a  new  value  for  d.  Try  d  =  26  in. 

then  j  =0.192 
a 

and  from  Diagram  2 


6  =  29.  7  in. 

This  value  is  sufficiently  close  so  as  to  require  no  further  revision. 
To  find  the  area  of  steel  required  first  obtain  j  from  the  right-hand  side  of  Diagram 

2  by  tracing  upward  from  /c  =  650  to  intersection  of  r-^  =  86.0  and  read  ;  =  0.913 

11 


CORRUGATED   BAR   COMPANY,  INC. 


M  1,728,000 

then  As  =  j^  =  (o.913)  (26)  (16,000)  =  4'55  Sq'  11L 

Example  2.  Given  a  T-beam  of  20  ft.  span,  ends  freely  supported,  <  =  4  in.,  d  =  2Q 
in.,  6  =  30  in.,  ^4»==4.0  sq.  in.  Find  the  total  load  per  foot  this  beam  will  carry  when 
n=  15  and/B  and/0  are  not  to  exceed  16,000  and  650  pounds  per  square  inch,  respectively, 


JL1-02 
d    20 

On  the  left  of  Diagram  4  from  the  intersection  of   ^=0.2  and  p  =  0.667%  read 

k  =  0  .  40  and  on  the  right  from  the  intersection  of  p  =  0  .  667%  and  k  =  0  .  40  read  j  =  0  .  912 
Me  =  Aafejd  =(4.0)  (16,000)  (0.912)  (20)  =  1,167,360  in.  Ib. 


=  650  (l  -  (2)(Q40)(20))  (30)  (4)  (0.912)  (20)  =  1,067,040  in.  Ib. 
The  resisting  moment  of  the  concrete,  being  less  than  that  of  the  steel,  will  govern 

the  carrying  capacity  of  the  beam.    Equating  the  external  moment  (M  =  -  wlz)  in 

o 

inch  pounds  to  the  resisting  moment  of  the  concrete  and  solving  for  w  we  find 

8M      (8)  (1,067,040) 
=  I2T*  ~   (12)  (20)  (20)   == 

Beams  Reinforced  for  Compression.  It  is  sometimes  desirable  or  necessary  to 
place  reinforcement  in  the  compression  side  of  a  beam  in  order  to  maintain  the  con- 
crete stress  within  safe  limits.  Continuous  beams  of  T  section  are  frequently  deficient 
in  concrete  area  at  the  supports,  where  due  to  the  reversal  of  moment,  the  stem  is  in 
compression.  When  the  stress  in  the  concrete  at  this  point  exceeds  that  specified,  the 
straight  bars  in  the  bottom  of  the  beam  may  be  carried  through  the  support  and 
utilized  as  compressive  reinforcement. 

A  continuous  T-beam  has  the  following  dimensions: 

t  =  6  in.,  6  =  30  in.,  d  =  34  in.,  b'=  14  in. 

The  negative  moment  is  2,400,000  in.  Ib.  It  will  be  assumed  that  the  working  stress 
in  the  concrete  at  the  center  of  the  beam  is  650  pounds  per  square  inch  which  may 
be  increased  15%  at  the  support,  in  accordance  with  recommendations  of  the  Joint 
Committee,  so  that  the  value  at  this  point  is  747  pounds  per  square  inch,  steel  stress 
16,000  pounds  per  square  inch.  Determine  the  amount  of  compression  steel  required. 

In  the  top  for  tension, 

2,400,000 


(16,000)  (I)  (34) 
Vv 


=  5.04  sq.  m. 


M_         2.400.000 
bd*      (14)  (34)  (34)  ~ 
Entering  Diagram  1  with  #=148,  we  find,  f or /8  =  16,000,  that  fc  =  805.   The  reduc- 

12 


USEFUL      DATA 


tion  of/c  to  747  will  then  be  —  ^-=  —  =   7.2%.  Entering  Diagram  5,  on  the  left 

margin,  with  7.2  and  moving  to  the  right  to  the  "concrete  curve,"  thence  downward, 
the  amount  of  compressive  steel  to  effect  the  reduction  in  /c  is  found  to  be  0.20%  or 
(14)  (34)  (0.002)  =0.95  sq.  in. 

Combined  Bending  and  Direct  Stress.  In  the  design  of  columns,  arch  rings, 
etc.,  the  resultant  of  the  external  forces  does  not  always  coincide  with  the  center  of 
gravity  of  the  cross  section  of  the  member.  In  such  cases  consideration  must  be  given 
to  the  combined  action  of  bending  and  direct  stress.  For  reinforced  concrete  members 
the  general  formula  for  extreme  fibre  stress  where  compression  exists  over  the  entire 
section,  is 

w  My 


W=  Total  direct  load. 

p0  =  Percentage  of  reinforcement  =  -~ 

y  =  Distance  from  center  of  gravity  of  section  to  extreme  fibre. 
7C  =  Moment  of  inertia  of  concrete  section  about  the  gravity  axis 
IB  =  Moment  of  inertia  of  steel  area  about  the  gravity  axis. 
The  other  symbols  are  as  given  in  the  standard  notation,  pages  5  and  6. 
It  is  in  the  case  of  rectangular  sections  with  symmetrical  reinforcement,  that  we 
most  frequently  meet  with  problems  involving  bending  and  direct  stress  and  Dia- 
grams 6,  7,   8a  and   8b,  will  be  found  to  greatly  facilitate  the  solution  of   such 
problems. 

In  the  case  of  a  homogeneous  material  no  tension  exists  on  the  cross  section  when 
the  resultant  falls  within  the  middle  third.  For  a  concrete  section  reinforced  with  steel 
bars  the  conditions  are  altered  somewhat  and  the  resultant  may  fall  slightly  outside 
the  middle  third  without  producing  tension  on  the  section.  In  those  cases  where  com- 
pression exists  over  the  whole  section  Diagram  6  may  be  employed,  but  where  there 
is  tension  over  part  of  the  section  Diagrams  7  and  8a  or  8b  should  be  used. 

Case  I.  No  Tension  on  the  Cross  Section.  Consider  a  column  18  inches 
square,  reinforced  with  4-1  in.  square  bars,  carrying  a  load  of  150,000  Ib.  concen- 
trated 1  in.  from  the  center  of  the  column.  Find  the  maximum  unit  stress  in  the 
concrete. 

Percentage  of  reinforcement,  p0  =  -r-8  =  QQ\  Qg)  =  1  •  23% 

The  eccentricity  z0=  1  in. 

and  y=Yg  =  0.0555 

Entering  Diagram  6  with  j  =  0 . 0555,  tracing  vertically  to  p0  =  1 . 23%  and  then  to 

the  left  margin  find  K'=  1 .09,  a  factor  by  which  the  average  unit  stress  must  be  multi- 
plied to  find  the  maximum  unit  stress. 

505  Ib.  per  sq.  in. 
13 


CORRUGATED   BAR   COMPANY,  INC. 


To  obtain  the  minimum  concrete  unit  stress  we  know  that  the  minimum  is  as  much 
below  the  average  as  the  maximum  is  above.   In  this  example  the  average  concrete  unit 

stress  is  f,     w     .  -  '        /1KWyl\  =  394  Ib.  per  sq.  in.  Thus  the  minimum  unit  stress  is 
—  ^J  ~r 


394-  (505-394)  =283  pounds  per  square  inch. 

Case  II.     Tension  on  the  Cross-Section.     Suppose  the  column  of  Case  I  had 
an  applied  moment  of  800,000  in.  Ib.  in  addition  to  an  axial  load  of  100,000  Ib.    Then 

M      800,000 

*0  =  JF  =  T6o66o  = 
•T-H-0-"4 

As  before  po=1.23%  entering  Diagram  7  with  ~  =  0.444,  tracing  vertically  to 

p0=1.23%,  then  to  the  left  margin,  k  =0.60.    Now  entering  Diagram  8a  with  this 
value  of  k  and  tracing  to  p0=  1  .  23%,  the  value  of  F  is  found  to  be  0.  139.   Then 

M  800,000 

Max''«=  w-  (0.139)  (18)  (18)  (18)  =  987  P0unds  per  Sq'  m' 
This  resulting  fibre  stress  is  larger  than  is  usually  permitted  and  would  necessitate 
a  redesign  of  the  column  section  in  order  to  reduce  the  stress  to  the  limit  allowable. 


14 


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15 


CORRUGATED      BAR      COMPANY,     INC. 


Percentage  of  Reinforcement 
0.3     0.4     0.5     0.6     0.7     0.8     0.9     1.0      1.1     1.2      1.3     1.4      1.5     1.6 

1.0  IlllllllillUJIIIIII IhlillllllllllllllLilllll       II  I  Mil  II  II     Mill  I  I  'I  0.0 


0.8 


50 


40 


0.5%  1.0% 

Percentage  of  Reinforcement 


DIAGRAM  1 
Coefficients  of  resistance  K  and  values  of  j  and  k  for  rectangular  beams. 


16 


USEFUL      DATA 


~hs  «. 
•S    ° 


.22 


17 


CORRUGATED   BAR   COMPANY,  INC. 


S   I   §   §   S   8   8 


od 


18 


USEFUL      DATA 


19 


CORRUGATED   BAR   COMPANY,   INC. 


Percentage  of  Compressive  Steel 
0.5% 1% 1.5% 


0.5%  1%  1.5% 

Percentage  of  Compressive  Steel 

DIAGRAM  5 
Compressive  reinforcement  of  beams. 


20 


USEFUL      DATA 

Values  of  ^ 
0.10        0.12       0.14 


0.16       0.18       0.20       0.22 


2.00 


1.90 


0.90 


0.90 


0         0.02      0.04       0.06       0.08       0.10       0.12       0.14       0.16       0.18       0.20       0.22 
Values  of  ^ 

DIAGRAM  6 

Bending  and  direct  stress. 

Values  of  K',  a  factor  by  which  the  average  stress  is  multiplied  to  obtain 
the  maximum  fibre  stress. 


21 


CORRUGATED      BAR      COMPANY,     INC. 


Values  of   ± 

0.17  0.18       0.20       0.22        0.24        0.26        0.28        0.30        0.32        0.34        0.36       0.38 
1.0 


0.4  0.6  0.8  1.0  1.2  1.4  1.6  1.8         2.0 


0.2 


0.1 


0.2 


0.1 


DIAGRAM  7 

Bending  and  direct  stress. 
Values  of  k,  the  ratio  of  distance  of  neutral  axis  from  extreme  fibre  to 

total  thickness  or  depth,  f,  when  d'  =  T£ 


22 


USEFUL      DATA 

Values  of  k 
0.9  0.8  0.7  0.6  0.5  0.4  0.3  0.2  O.I 


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Values  of  k 


DIAGRAM  8a 
Bending  and  direct  stress. 


M 


Values  of  coefficient  F  in  formula  for  obtaining  extreme  fibre  stress  /c  =  "r 


23 


CORRUGATED   BAR   COMPANY,  INC. 


c 

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0.30 
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0.26 

0.24 

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1 

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0.14 

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Case  II 
Tension  over  part 
of  Section 

u 

&Ur 

1  ^   J 

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E 

K—  -fct—  * 

0.12 

0. 

Va 

9                 0.8                 0.7                 0.6                  0.5                 0.4                 0.3                0.2 
Values  of  fc 

DIAGRAM  8b 
Bending  and  direct  stress. 

tlues  of  coefficient  F  in  formula  for  obtaining  extreme  fibre  stress  fc=^r- 
1                                                  W 
when  d'=  —  < 

24 


USEFUL      DATA 


1.0 


0.9 


"S 

n 


0.8 


^ 


0.7 


0.6 


0.5 


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Ratio  -^1- 

DlAGRAM  9 

Curve  showing  distribution  of  load  for  rectangular  slabs  supported 
at  the  four  edges. 


25 


CORRUGATED   BAR   COMPANY,  INC. 


GENERAL  FORMULAS  FOR   BEAMS 

REACTIONS,   BENDING  MOMENTS,    SHEARS   AND   DEFLECTIONS 
CAUSED    BY    VARIOUS   APPLIED    LOADS 

The  classes  of  beam  loading  given  on  the  following  pages  cover  the  majority  of 
cases  occurring  in  reinforced  concrete  design.  The  formulas  may  be  applied  to  a  beam 
of  any  material,  although  it  should  be  noted  that  those  for  deflection  and  maximum 
safe  load  require  modification  for  use  in  connection  with  reinforced  concrete  beams. 

In  the  application  of  deflection  and  maximum  load  formulas  to  reinforced  concrete 
beams  account  must  be  taken  of  the  fact  that  the  moment  of  inertia  of  the  section 
and  the  modulus  of  elasticity  of  the  material  enters  into  the  computations,  thereby 
introducing  elements  of  uncertainty  that  do  not  exist  in  the  case  of  homogeneous 
beams,  at  least  not  within  the  limits  of  working  stresses.  Bearing  this  fact  in  mind  it 
will  be  necessary  to  make  certain  assumptions  before  applying  these  formulas.  These 
assumptions  may  be  stated  briefly  as  follows: 

1.  The  moment  of  inertia  is  considered  substantially  uniform  throughout  the 
length  of  the  beam,  and  shall  be  taken  as  that  of  the  section  of  the  beam  at  the  center 
of  the  span. 

2.  The  section  shall  be  considered  intact  from  top  of  beam  to  center  of  steel. 

3.  The  modulus  of  elasticity  of  the  concrete  shall  be  taken  as  the  average  or  secant 
modulus  up  to  the  working  compressive  stress. 

For  such  a  beam  the  moment  of  inertia  of  a  section  is  the  moment  of  inertia  of  the 
concrete  about  the  neutral  axis  plus  n  times  the  moment  of  inertia  of  the  steel  about  the 
same  axis,  or 


-fc>     for  rectangular  beams. 


-fc)2    for  T-beams 


The  value  of  the  modulus  of  elasticity  to  use  in  the  deflection  formula  is  that  of 
the  concrete,  or 


It  is  recommended,  from  the  consideration  of  test  data,  that  8  or  10  be  used  for  n 
to  secure  fair  agreement  between  computed  and  measured  deflection.  A  more  com- 
plete discussion  of  the  subject  of  deflection  of  reinforced  concrete  beams  will  be  found 
in  "Principles  of  Reinforced  Concrete  Construction"  by  Turneaure  and  Maurer. 

The  formulas,  pages  28  to  37  inclusive,  pertain  to  superimposed  loads  only,  the 
weight  of  the  beam  itself  being  neglected.  This  fact  should  not  be  overlooked  when 
applying  the  formulas  in  practice.  The  maximum  safe  load  formulas  apply  only  to 
homogeneous  beams.  To  obtain  the  maximum  safe  load  for  a  reinforced  concrete 
beam,  equate  the  maximum  external  bending  moment,  including  the  bending  moment 
of  the  weight  of  the  beam,  to  the  internal  resisting  moment  of  the  section  and  solve 
for  wm. 

26 


USEFUL      DATA 


NOTATION.  The  following  notation  has  been  adopted  in  the  formulas: 
P,  p      =  Concentrated  loads  in  pounds. 

w     =  Superimposed  load  in  pounds  per  unit  length  of  beam  or  slab. 
W    =  Superimposed  load  supported  by  beam  or  slab  in  pounds. 
I       =  Length  of  beam  in  feet. 
L     —  Length  of  beam  in  inches. 
RI,  RI    =  Reactions  at  supports  of  beam,  in  pounds. 

Vx    =  Total  transverse  shear  in  pounds,  at  distance  x. 

Vm  —  Total  maximum  transverse  shear  in  pounds. 

Mm  =  Maximum  positive  external  bending  moment  in  foot-pounds. 

M'm  =  Maximum  negative  external  bending  moment  in  foot-pounds. 

x0     =  Distance  in  feet  to  point  of  zero  shear,  or  to  Mm. 

wm    =  Maximum  safe  load  in  pounds  per  unit  length  of  beam  or  slab  for  load 

distribution  indicated  in  each  case. 
Pm  =  Maximum  safe  concentrated  load  in  pounds. 
/       =  Working  unit-stress  in  flexure,  in  pounds  per  square  inch.   (This  does  not 

apply  to  reinforced  concrete  beams.) 
/      =  Moment  of  inertia  of  cross-section  in  inches4. 
S      =  Section  modulus  of  cross-section  in  inches3. 

(Thic  does  not  apply  to  reinforced  concrete  beams.) 
D     =  Maximum  deflection  in  inches. 
y      =  Distance  in  feet  to  point  of  maximum  deflection  D. 

NOTE:  When  substituting  numerical  values  in  formulas  all  quantities  must  be 
expressed  in  the  same  units.  For  example  in  formulas  for  deflection  E 
and  /  are  usually  expressed  in  terms  of  inches,  therefore  w  must  be 
taken  as  pounds  per  linear  inch  and  L  in  inches. 


j 


DIVERSITY  OF  CALIFORNIA 
&TMENT  OF  CIVIL  ENGINES*;  IG 
BERKELEY.  CALlr  OHNIA 


27 


CORRUGATED   BAR   COMPANY,  INC. 


1.    Cantilever  Beam.     Concentrated  load. 


! 
Jfj 


L 


x  =P(x-a) 
m  =  P(Z-a) 


Moment  Diagram 


D     =^-_(2L3-3aL2+a3)  (Right  end) 


f 

Vm\ 


Sh4r  Diagram        D&    =     P    (L-a)*     (At  load  P) 
6tiil 


2.     Cantilever  Beam.     Uniformly  distributed  load, 


Km 


Moment  Diagram 


;  Shear  Diagram 


It     =  w=wl=Vm 

7TL       =WX 

b*«! 
^-f-f 

Pm  =  6T2" 


3.     Cantilever  Beam.     Load  increasing  uniformly  to  fixed  end. 

,w 


Moment  Diagram  _  wl2  _  W( 


21 
wx* 
61 


Shear  Diagram     ^      ~~  or\j?j 


28 


USEFUL,      DATA 


4.     Cantilever  Beam.     Load  increasing  uniformly  to  free  end. 


a,  -ip-=f-r. 

F,  -f  (a-,) 


Moment  Diagram 

L/'«"x 


4/2 

Shear  Diagram     n  11     wL* 

=  120  17 


5.    Beam  Supported  at  Ends.      Concentrated  load  near  one  end. 
t<-— a — -** & •». 


Pb 


Pbx 


Moment  Diagram 


ZEIL 


Shear  Diagram    y       =  -  -\/36(/+a)      a  <   b  and  ?/  on  same 

<J       '  ci/-lf»  f\f   Innrl   n  c  /) 


side  of  load  as  6. 


6.    Beam  Supported  at  Ends.     Concentrated  load  at  center. 


29 


CORRUGATED   BAR   COMPANY,  INC. 


7.     Beam  Supported  at  Ends.    Two  unequal  and  unsymmetrical  concentrated  loads 
M«    >-£-*• 


Fx    =Ri— PI  for  x  between  loads. 

.Moment  Fm  =  Maximum  Reaction. 

Diagram  _  L  _ 

/O  !  I  I  JW  I  I  (W\  !  ^*  =  PiT(J-z)+P2-7-  for  z  between  loads. 

1rulli1lllltmlK!  *  * 


Mm  =  Greater  of  Jl/i  and  M2 


8.     Beam  Supported  at  Ends.     Two  equal  unsymmetrical  concentrated  loads. 
—  6—*  p 

IP  R<    =^(l-a-\-b) 


Fx  =Ri  —  P  for  #  between  loads. 

Fm  =  Maximum  Reaction 
Moment  p 

Diagram     M*  =  -j  (al  —  ax-}-bx)  for  x  between  loads. 


|p  Shear  Diagram  ' 

— -iyx      lfm  =  Greater  of  Mi  and  3/2 

P°  =126?i-i,+a)(wben''>a) 
9.     Beams  Supported  at  Ends.     Two  equal  symmetrical  concentrated  loads. 

Fx   =0  for  x  between  loads. 

MX.  =Mm=Pa  for  x  between  loads. 


RA 

\<r—X- »> 

L j. 


P     - 
^m 


• 
12o 


Moment  j)      = 

Diagram 


2-4a2) 


At  center. 


Shear  Diagram 

Q* 


Whena=- 


f.-5 

23 


648    £/ 


30 


USEFUL      DATA 


10.    Beam  Supported  at  Ends.  Three  unequal  unsymmetrical  concentrated  loads. 

*-a  r»*"~   6r- 

Le0    | M 62— 


a3-  -------  -; 

IP.      Jft 


Moment 
|K  Diagram 


2Pb     _  _  2Pa 

~T    K2~~T 


Vm  =  Greater  Reaction 

Mt^jSPb-Pfa-ad 


Mm  =  Greatest  of  Mi  M*  and  Ms 

=  MZ  if  Pi  <  Ri  when  (Pi+P2)>Ri 
=  M3  if  P3  >  Rz 


11.     Beam  Supported  at  Ends.     Three  equal  concentrated  loads  placed  as  shown. 

K..l..¥-.X-Jf.J...^-J.-^ 
I  4  K  I-4  fr  I 
* 


M     =Pl 

Mm        2 

P      _  fS 
^m  ~Ql 

Shear  Diagram     D     =19     PU  ^  ^^ 
oo4     £// 


12.    Beam  Supported  at  Ends.     Uniform  load  partially  distributed. 


D  agram 


Shear  Diagram 

— *, 


...ruiMiii.-?2 


31 


CORRUGATED   BAR   COMPANY,  INC. 


13.    Beam  Supported  at  Ends.     Uniform  load  partially  discontinuous. 


21 


Rz 


Moment  y     =  Greater  Reaction 

Diagram 


Shear  Diagram     ^     =  j_a_6+ *1  (when  6>a) 


«.-------^>  i^g 

14.     Beam  Supported  at  Ends.     Uniformly  distributed  load. 


Moment 

Diagram 


wl2Wl 


Shear  Diagram     Z)      = 


3/2 
334 


15.     Beam  Supported  at  Ends.     Load  increasing  uniformly  to  center. 


Moment 


Shear  Diagram 


wl* 


,. 

Diagram        Mm  = 


32 


USEFUL      DATA 


16.     Beam  Supported  at  Ends.     Load  decreasing  uniformly  to  center. 


17.    Beam  Supported  at  Ends.     Load  increasing  uniformly  to  one  end. 


x0    =0.5774/ 
aJ  =  1.3/S 

x    Shear  Diagram       2/       =  0 . 519  Z 
D     =0.00652 


^ 


18.    Beam  Fixed  at  Ends.    Load  increasing  uniformly  to  center. 


wl 
=  «'=! 


32 


33 


CORRUGATED      BAR      COMPANY,     INC. 


19.    Beam  Fixed  at  Ends.     Load  decreasing  uniformly  to  center. 


id 
4 


JT.-Jf.- 


g 


20.     Beam  Supported  at  Ends.     Uniformly  distributed  load  plus  load  increasing 
uniformly  to  one  end. 


TT-^  Moment 

D  agram 


Shear  Diagram 


Approx. 
between  0  .  50  /  and  0  .  58  / 


21.    Beam  Fixed  at  One  End,  Supported  at  Other.     Concentrated  load. 


,    . 


fe-P(z-a)    For  x  >a 


Diagram         x\      = 


p 

Shear  Diagram         M 'm  =  0/2  (^2  ~  a3) 

"*  PL3 

_  j*2          when  y  =  a=  0 . 414Z,  D  =  0 . 0098  -^~ 

34 


USEFUL      DATA 


22.    Beam  Fixed  at  One  End,  Supported  at  Other.     Load  increasing  uniformly 


IV 


Rl 

k i- 


to  fixed  end. 


To 


10 


,__Moment  y      =  ^  _^ 

I  iV>>w      rUnornrv,  JQ  <^ 


^ X- 


"To 


Shear  rjiagram       Mm  =  0 . 03  wl* 


x'     =0.775/ 
23.     Beam  Fixed  at  One  End,  Supported  at  Other.    Uniformly  distributed  load. 

Tt  &  f 


fpi       ! 3 

•^  !     L^t-J 


*--  x— >i 
ly=0.4215I>| 

-z ->, 


Moment 
Diagram 


wx 

T 

9 


Shear  Diagram 


x'     =  ^-   I 
y      ='0.4215Z 
D     = 


24.    Beam  Fixed  at  Ends.     Load  increasing  uniformly  to  one  end. 

=  7i£/ 

20 

ft       =  T^TT 


Moment 

Diagram 


_ 
1    "  20  ~   21 


Afm! 


: 
I 

Shear  Diagram 


3wlx      wP      wx3 
20         30        6/ 


Mm=0.0215w;/2 


35 


CORRUGATED   BAR   COMPANY,  INC. 


25.    Beam  Fixed  at  Ends.     Uniformly  distributed  load. 


Moment  Diagram        M*  =          *"* 


wl2 


Shear  Diagram 


,.     2 


24 
x0     =  2l 


D       - 

384  El 


26.     Beam  Fixed  at  Ends.     Concentrated  load  at  center. 

u~4-~* 

1          Ip 

:i T 


Rz 


x  =pa;—  -       between  ft  and 


\Moment  Diagram 


1  /  3 

2  P  (  4 


-fij 


Shear  Diagram 

Tfc 


Z)     = 


192 


27.    Beam  Fixed  at  Ends.     Concentrated  load. 


h    =P 


-a)2  (2o+0 


^C1     i 

,:$*«— a; —>> 


-4_/ 


Fx    =  7?i  between  R\  and  P 
^Moment  Diagram       FXj  =  jRa  between  P  and  /?2 

3/x  =^iX+M'm  between  RI  and  P 


=  -  P 


a(Z-a)2 


Shear  Dis 


USEFUL      DATA 


28.    Beams  Supported  at  Ends.     Concentrated  moving  loads. 
Case  1  /-N 


*L_ 


Max.  V  when  x=o 
Max.  M  when  x=  - 


:fli  =  P 

:^(atP) 


Case  2 


4 

K— -X 


Max.  F  when  x  = 


Max.  M  when  x  =    (2J  -  a) 


y(2/-a) 


=       (2/-a) 


When  a  exceeds  0.586/,  use  Case  1  for  Mm. 


CaseS     j<- 


Max.  V  when  x=a 
Max.  M  when  x  = 


>=  |  (3*-4a) 


j J         When  a  exceeds  0.45J,  use  Case  2  for  Mm. 

-  °  -»i  Max.  V  when  z=o  Fm  =  Ri  =  *.   , 

F -*T^ -^ a        Max.  M  whenx=  -  I Z— ^-p  I    Mm=—^P 

^ "____  l  J        Maximum  moment  may  occur  under  one  load  only. 

Case  5        ra  ->ta-*-a  *i  MaX*  V  Whe°  X=a 

QQQGv^        Max.  If  when  x=  j(2/-a)    , 
^F  >2  4/ 

When  a  exceeds  0.268/,  use  Case  3  for  Mm. 

Z    -— — — — ^i 

Max.  V  when  x=a 

®  *•     ^          j 

/zf~  "t«2     Max.  M  when  x=  -  +  ^ 

^ x >-j  •*• 

t^. z >j         JT   _  g2^P      p      Maximum  moment  may  occur  for 

I  two  loads  only.  See  Case  2. 

Max.  V  when  x=b.    If  -  >  ^  use  Case  6. 

Ca^r1^-''-^--  a  -^-^  2p  P 

jR^.._  x  ™->i  T2     Max.  M  when  x  =  i  (21- a)  I  Mm=  "^  (2/-a)I-p6 

Maximum  moment  may  occur  as  for  Case  6. 
37 


CORRUGATED   BAR   COMPANY,  INC. 


MOMENTS   AND    SHEARS   FOR   CONTINUOUS 
BEAMS 

The  moment  factors  commonly  specified  for  continuous  beams  assume  equal  spans 
and  uniform  loads.  While  these  factors  are  within  safe  limits  for  the  usual  conditions 
met  with  in  building  design,  cases  arise  where  it  is  advisable  to  investigate  the  actual 
moments  and  shears  produced,  through  inequality  of  span  and  load,  by  the  theorem  of 
three  moments. 

This  theorem  may  be  employed  in  problems  involving  either  uniform  or  concentrated 
loads  or  combinations  of  the  two,  but  a  full  discussion  of  the  theory  involved  would 
be  out  of  place  in  a  book  of  this  character  and,  therefore,  only  a  brief  statement  cov- 
ering its  application  will  be  given. 

In  the  formulas  and  diagrams  which  follow  it  is  assumed  that  the  moment  of  inertia 
is  constant  throughout  the  length  of  the  beam  and  that  the  supports  retain  their  same 
relative  position  after  the  beam  is  loaded  as  before. 

UNIFORM  LOAD 

For  uniform  load  the  theorem  is  expressed  by  the  formula, 


Mi w 


FIG.  4 

The  equation  as  written  applies  to  the  moments  at  the  supports  in  span  li  and  h; 
by  increasing  all  the  subscripts  by  one  it  will  apply  to  spans  12  and  h  and  so  on  for  as 
many  spans  as  there  are  in  the  structure.  It  will  thus  be  seen  that  there  may  be  ob- 
tained as  many  equations  as  there  are  unknown  moments,  assuming  that  the  moments 
at  the  first  and  last  support  are  zero  or  their  values  are  known.  Having  obtained  the 
moments  at  the  supports,  the  shears  and  moments  at  any  other  section  of  the  beam 
may  be  found  by  the  following  equations. 

Consider  for  example,  spans  h  and  /2  in  Fig.  4. 

v    =  M2—Mi     w^i 
li        h   2 


z  .     a 

~   2 


The  reaction  at  any  support  (Ri}  Rz,  etc.)  will  be  equal  to  the  shear  on  its  right 
plus  that  on  its  left  with  the  sign  reversed. 


USEFUL      DATA 

The  distance  to  the  point  of  zero  shear,  provided  the  shear  changes  sign  in  the  span,  is 

Xi  =  — -  for  span  l\ 

Wi 

Xz  =  —  for  span  It 

The  bending  moment  at  this  point, 

M  =  Mi+ViXi l^-  for  span  li 


M=M2+Vzx2-  for  span  /, 

If  the  sign  of  this  moment  is  plus,  it  is  the  maximum  positive  moment.  If  the  sign 
is  minus,  it  is  the  minimum  negative  moment  and  indicates  that  no  positive  moment 
exists  at  any  point  of  the  span. 

By  changing  the  subscripts  as  previously  mentioned  the  formulas  may  be  applied 
to  any  span. 

CONCENTRATED   LOADS 

For  concentrated  loads  the  theorem  is  expressed  by  the  formula, 


. 

r t*i* 

$2k*  '4     *--*•  n 


^  r  i  t  t  i 

« Xl y  I— *2— ' ' 

n         i        5F2------*       535- / -4F4--- ir -T 

FIG.  5 
Applied  to  spans  h  and  h,  Fig.  5,  the  formula  would  be  written  as  follows: 


The  shears  will  then  be: 


Knowing  the  moments  at  the  supports,  the  shears  and  moments  at  any  section  may 
be  obtained  as  in  the  case  of  continuous  beams  with  uniformly  distributed  loads. 

Careful  attention  must  be  paid  to  the  use  of  the  proper  algebraic  signs  in  the  fore- 
going equations. 

Equal  Spans.  Uniform  load  over  all  spans:  Diagram  10,  page  45,  gives 
moment  coefficients  of  wl2  at  critical  sections  of  continuous  beams  of  from  two  to 

39 


CORRUGATED   BAR   COMPANY,  INC. 


seven  spans  and  Diagram  11  gives  shear  coefficients  of  wl  at  supports  for  the  same 
case. 

Example.    For  a  beam  of  three  spans  the  negative  moment  at  the  first  interior 

support  is  0  .  IQwl2.  The  shear  at  the  end  of  the  middle  span  is  TTJW/  and  at  the  inner 
support  of  the  end  span  it  is  TQW^- 

Equal  Concentrated  Loads  on  All  Spans:  Diagram  12,  page  46,  shows  three 
cases  of  loading.  (1)  Loads  at  middle  points.  (2)  Loads  at  third  points.  (3) 
Loads  at  middle  and  quarter  points.  The  full  irregular  line  is  the  moment  curve  and 
the  broken  line  represents  the  shear  line  for  each  case  of  loading.  The  ordinates  to  the 
moment  line  are  coefficients  of  PI  and  the  ordinates  to  the  shear  line  are  coefficients  of 
P.  The  numerical  coefficients  are  given  at  critical  sections. 

Example:  At  the  central  span  of  a  five-span  girder  loaded  at  the  third  points,  the 
negative  moment  at  the  adjacent  support  is  0.211  PI;  the  positive  moment  at  either 
of  the  loads  is  0.  122PZ  and  the  reaction  at  the  adjacent  support  is  1.93P. 

The  moments  and  shears  of  any  uniform  load  should  be  combined  with  those  of  the 
concentrated  loads  on  the  girder. 

Partial  Uniform  Load:  Diagrams  13,  14,  15  and  16,  pages  47  and  48,  for  two 
and  three  span  beams,  give  moment  and  shear  coefficients  that  are  maximum  for  the 
indicated  positions  of  the  uniform  load;  the  ends  of  the  beams  being  either  free  or 
fixed. 

Unequal  Spans.  Uniform  Load:  In  the  design  of  schools,  hospitals,  hotels 
public  buildings,  garages  and  shop  buildings,  the  layout  usually  involves  continuous 
beams  of  unequal  span.  The  application  of  the  three  moment  theorem  in  such 
cases  can  best  be  illustrated  by  means  of  problems. 


M2  \W2  MS  Wz  Mj-0 


fe  ------------  „.»..  .........  ...zdb-^-4i  _______  ,,.,,  ...........  4 

Bl  #2  «3  #4 

Live  load  per  foot  of  span  =  800  Ibs. 
Dead    ........      "    =1000  " 

FIG.  6 

Problem  I.  Assume  a  beam  of  three  unequal  spans  as  shown  in  Fig.  6,  carrying  a 
live  load  of  800  pounds  per  linear  foot  and  a  dead  load  of  1,000  pounds  per  linear  foot. 
Find  the  critical  moments,  shears  and  reactions,  the  ends  being  assumed  simply 
supported. 

Casel 


l« h.-.  __>!<—  i2~~ >|«-.  — /3--- 

Live  Load  on  All  Spans.    The  ends  being  simply  supported  Mi  =  M4  =  Q. 
The  moments  Mt  and  M»  at  the  intermediate  supports  can  now  be  found. 

40 


USEFUL      DATA 


From  page  38, 


Substituting  numerical  values  in  these  two  equations: 

7MM-10M.  =  -  (1-8°°4)  (25)3  -  (1'80°4)  (10)°  =  -7.481.250  .....  (1) 

=  -4.050.000  .....  (2) 


Multiplying  equation  (1)  by  6  and  subtracting  equation  (2) 

41(W2=  -40,837,500 

M2=  -99,604  ft.  Ib.  and  we  find  M3=  -50,899  ft.  Ib. 

Substituting  in  Eq.  (2)  Ms=  -50,899  ft.  Ib. 


From  page  38,  Vl= 


(-99,604)      (1.800)  (25) 
=  -  25  --  '  --  2  -  = 

F'a=  Fx-  Wi=  18,516-  (1,800)  (25) 


(-50.899)-(-99,604)  ,   (1,800)  (10) 
=  ^  -  —  - 

F'3=F2-W2=13,870-(1,800)  (10) 

T,         Mi  —  M3   .   Wsk 


R,  =F2+F'2=13,870+26,484=40,3541b. 
R3  =73+^3=20,545+4,130=24,675  Ib. 
R,  =F'4=  15,455  Ibs. 

Distance  from  left  support  to  point  of  zero  shear, 
FI     18,516      ,~  f^. 


=  -26,484  Ib. 


=  -4,130  Ib. 


-15,455  Ib. 


=    7.71  ft.  for  span 


41 


CORRUGATED   BAR   COMPANY,  INC. 


Moment  at  point  xit  M  = 


=  (18,516)  (10.29)  -  (1'80°)(1Q-29)2  =  +95,243  ft.  Ib. 

This  is  the  maximum  positive  moment  in  span  /i  for  this  condition  of  loading. 
Moment  at  point  x^, 


,,      ,,   .  T7 

M  =  M2+  Vzxt 

=  (  -99,604)  +(13,870)  (7.71)  -  t1'800)  (7.71)2  =  _46,166  ft.  Ib. 

2 

This  is  the  minimum  negative  moment  in  span  4  and  indicates  that  no  positive  mo- 
ment exists  in  the  span  for  this  condition  of  loading,  a  point  that  is  worthy  of 
notice,  as  quite  commonly  this  span  is  designed  for  positive  moment  only.  Moment 
at  point  a?3, 


=  (-50,899)  +(20,545)  (11.41)  -  (1>8°°)^11-41)2=  +66.350  ft.  Ib. 

If  the  beam  is  subjected  to  partial  loading  larger  moments,  shears  and  reactions  may 
be  obtained  than  in  Case  1.  The  maximum  values  for  this  problem  are  given  in  the 
following  cases  when  the  live  load  is  placed  as  shown. 

Case  2 

Max.  M,  =  -  103,506  ft.  Ib. 
Max.  F'2=  -  26,640  Ib. 
Max.  F2=  +  16,992  Ib. 
Max.  R2  =+  43,632  Ib. 


---„ .t 


CaseS 

Max.  M3=-  58,521ft.  Ib. 
Max.  F'3=-     9,465  Ib. 

Max.  F3=+  20,926  Ib. 

Max.  R3  =  +  30,391  Ib. 


t PliMM 

I h J^~ 


Max.  positive  moment  in  span  /i=  +  97,300  ft.  Ib. 

Case  4  Max.  positive  moment  in  span  Z3=  +  67,300  ft.  Ib. 

Max.  F!  =  +  18,614  Ib. 
Max.  F'4=-  15,606  Ib. 
,    Max.  Ri  =  +  18,614  Ib. 
Max.  R<=+  15,606  Ib. 

Case  4  also  gives  the  position  of  live  load  for  maximum  negative  moment  at  the  center 
of  span  Z2. 

42 


USEFUL      DATA 


Problem  II.  Assume  a  beam  having  a  long  central  span  and  two  shorter  end 
spans  of  equal  length,  as  shown  in  Fig.  7,  carrying  a  live  load  of  2,500  pounds  per 
linear  foot  and  a  dead  load  of  2,200  pounds  per  linear  foot.  To  find  the  critical  moments, 
shears  and  reactions,  assuming  the  ends  simply  supported. 


\w\ 


1 


MS 


IX  v'\vz  ,  vAv3  , 

[* jI=20'- ^ 12=40'- >|* Ji=20'- 


Live  load  per  ft.  of  span  =  2500  Ib. 

Dead -2200  " 

FlG.  7 

The  solution  of  this  problem  involves  the  same  procedure  as  that  carried  out  in 
detail  for  Problem  I,  Case  1,  and,  therefore,  the  results  only  are  tabulated  below  for 
the  various  cases  of  critical  loading. 

Case  1 


ll I miiiiiiiiiimiiimmiii .  


Case  2 


Mz  =  M3=-  528,750  ft.  Ib. 
Positive  moment  at  point  Xi  =  +  44,978  ft.  Ib. 
Positive  moment  at  point  a?2=  +411,250  ft.  Ib. 
F!=  +20,562  Ibs.  F'2  =  -73,438  Ibs.  F2  =  +94,000  Ib. 

Rt=     20,562  Ibs.     fl2=  167,438  Ib. 


Max.  M2  =-  544,375  ft.  Ib. 

Max.  F'2=-  74,219  Ib. 

Max.  F2=+  95,562  Ib. 
— ^  Max.  Jk  = +169,781  Ib. 
=  -  2,094  Ib. 


— 12 

NOTE. — This  loading  gives  negative  reaction, 
Case  3 


Max.  positive  moment  in 
j.____ir— „»!<-.        12 ^____.jr-_._>!     gpan  ^+442,500  ft.  Ib. 

NOTE. — This  loading  gives  negative  reactions  Ri  and  R4=  —2,875  Ib. 


Case  4 


—  -        1 

1 

T 

_;,  ^If.  ;0  ^ 

' 

Max.  positive  moment  in 
span  Zi= +116,294  ft.  Ib. 
Max.  F!  = +33,063  Ib. 
Max.  JRi  =  +33,063  Ib. 


43 


CORRUGATED   BAR   COMPANY,  INC. 


The  condition  of  simply  supported  ends  assumed  in  Problems  I  and  II  is  that  which 
occurs  when  the  beam  frames  into  a  brick  wall.  If,  however,  the  ends  frame  into  a 
column  or  girder,  the  moment  at  the  end  support  will  not  equal  zero,  but  will  have  a 

value  depending  upon  the  degree  of  fixity.   This  may  be  as  large  as  —^  where  small 
beams  frame  into  heavy  columns.    For  ordinary  conditions  the  Joint  Committee 

recommends  a  value  of  rr^- 
16 

We  will  now  take  Problem  II,  Case  1,  and  substitute  for  MI,  a  value  -ry-  and  for 

72 

3/4,  -T7T-  and  note  the  effect  on  the  various  moments  and  shears. 
16 

-117,500  ft.  ,b. 


, 

From  symmetry  Mz=Ms 


Inserting  numerical  values, 
(-117,500) 


160M2  =  (-9,400,000-75,200,000)+2,350,000 
(-84,600,000+2,350,000) 


,140fioff  1K 
—  514,063  ft.  Ib. 


Fi  =  (-514,063)  -(-117,500)  +  (4,700)  (20) 

20  2 

F'2=  27,172-  (4,700)  (20)  =  -66,828  Ib. 
Fj  =  (-514,063)-(-514,063)  }  (4,700)  (40) 

&  =  27,172  Ib. 

Rz  =  94,000+66,828  =  160,828  Ib. 

_  27,172  _ 
Xl  """ 


Moment  at  xlt  M  =  (-117,500)  +  (27,172)  (5.78)  -  (4>700)  ^  '78)2  =  -38,955ft.  Ib. 
94,000 

=20ft' 


Moment  at  x2,M  =  (-514,063)  +(94,000)  (20)-      >  2  =  +  425,937  ft.  Ib. 

It  will  be  noted  that  for  Problem  II,  Case  1,  with  the  ends  partially  restrained, 
negative  moment  exists  throughout  span  l\. 


44 


USEFUL      DATA 


DIAGRAM  10 

Moment  coefficients  of  w/2  for  continuous  beams  of  equal  spans  supported  at  the 
ends  and  uniformly  loaded. 

12 
ots  615^  sTo 

1  2  3 


17  |15  13J13 

28  28~ 

23 


0  [16  23|20  18T19  197*18  20J23  15|~0 

38  38  38  38  38  38 


63t56  49f61  53^53  6lf«9  55^63  o 

104  104  104  104  104  104 


75s6        660 
142          142          142          142          142          142          142          142 

DIAGRAM  11 

Shear  coefficients  of  wl  for  continuous  beams  of  equal  spans  supported  at  the 
ends  and  uniformly  loaded. 

45 


CORRUGATED   BAR   COMPANY,  INC. 


^qf^] 

I  <-.££ 


.31!^ 


7        .69; 
p  . 


.31 


Loads  at  Middle  Points 


3»£2]fiSLmrifl^ 


.73; 


..^ptM* 


,244 


"        - 


Loads  at  Third  Points 


U^394 

1.60 

Loads  at  Middle  and  Quarter  Points 

DIAGRAM  12 

Moment  coefficient  of  PI  and  shear  coefficient  of  P  for  continuous  beams  of  equal 
spans  supported  at  the  ends  and  loaded  as  indicated. 


46 


USEFUL      DATA 


w  pounds  per  foot  --, 


Ri 


\\ 

1^.10 


Moment  and  Shear  Diagram 
Supported  Ends 

,.054  wl2 


.021  wJ2 


Moment  and  Shear  Diagram 
Fixed  Ends 

DIAGRAM  13 

Moment  and  shear  coefficients  for  continuous  beams  of  two   equal   spans  with 
uniformly  distributed  load  on  one  span  only. 


w  pounds  per  foot., 


w  pounds  per  foot  -, 


TWl 


,059  w*2 


Moment  and  Shear  Diagram 
Supported  Ends      ! 


.028  wl2 


ITTTrK     «--r 


jj.m  wl^ 

Rl 


•r 


Moment  and  Shear  Diagram 
Fixed  Ends 


DIAGRAM  14 

Moment  and  shear  coefficients  for  continuous  beams  of  three  equal  spans  with 
uniformly  distributed  load  on  two  end  spans  only. 


47 


CORRUGATED      BAR      COMPANY,     INC. 


w  pounds  per  foot   «, 


Moment  and  Shear  Diagram 
Supported  Ends 


Moment  and  Shear  Diagram 
Fixed  Ends 

DIAGRAM  15 

Moment  and  shear  coefficients  for  continuous  beams  of  three  equal  spans  with 
uniformly  distributed  load  on  center  span  only. 

„.  w  pounds  per  foot^  ^ 


r:078  wl2 


"BI 


,'039^2 


Moment  and  Shear  Diagram 
Supported  Ends 


.022  wZ  2., 


Moment  and  Shear  Diagram 
Fixed  Ends 

DIAGRAM  16 

Moment  and  shear  coefficients  for  continuous  beams  of  three  equal  spans  with 
uniformly  distributed  load  on  center  and  one  end  span  only. 


48 


USEFUL      DATA 


CONTENTS  OF  STORAGE  WAREHOUSES 


Material 

Weights 
per 
Cubic  Foot 
of  Space, 
Pounds 

Height 
of  Pile, 
Feet 

Weights 
per 
Square  Foot 
of  Floor, 
Pounds 

Recom- 
mended 
Live  Loads, 
Pounds  per 
Square  Foot 

GROCERIES,  WINES,  LIQUORS,  ETC. 

Beans,  in  bags  

40 

8 

320 

Canned  Goods,  in  cases  

58 

6 

348 

Coffee,  Roasted,  in  bags     .... 

33 

8 

264 

Coffee,  Green,  in  bags     

39 

8 

312 

Dates,  in  cases     

55 

6 

330 

Figs,  in  cases     .    .        ... 

74 

5 

370 

Flour,  in  barrels 

40 

5 

200 

Molasses,  in  barrels     

48 

5 

240 

250  to  300 

Rice,  in  bags     

58 

6 

348 

Sal  Soda,  in  barrels      

46 

5 

230 

Salt,  in  bags  

70 

5 

350 

__~  —  -  — 

Soap  Powder,  in  cases     

38 

8 

304 

>pr 

Starch,  in  barrels     ... 

25 

6 

150 

Sugar,  in  barrels       

43 

5 

215 

Sugar,  in  cases  

51 

6 

306 

Tea,  in  chests    

25 

8 

200 

Wines  and  Liquors,  in  barrels    .    . 

38 

6 

228 

DRY  GOODS,  COTTON,  WOOL,  ETC. 

Burlap,  in  bales    

43 

6 

258 

Coir  Yarn,  in  bales  

33 

8 

264 

Cotton,  in  bales,  compressed      .    . 

18 

8 

144 

Cotton  Bleached  Goods,  in  cases  . 

28 

8 

224 

Cotton  Flannel,  in  cases     .... 

12 

8 

96 

Cotton  Sheeting,  in  cases   .... 

23 

8 

184 

Cotton  Yarn,  in  cases     

25 

8 

200 

Excelsior,  compressed      .       ... 

19 

8 

152 

Hemp,  Italian,  compressed    .    .    . 

22 

8 

176 

Hemp,  Manila,  compressed    .    .    . 

30 

8 

240 

200  to  250 

Jute,  compressed  .    .    . 

41 

8 

328 

Linen  Damask,  in  cases  

50 

5 

250 

Linen  Goods,  in  cases     .... 

30 

8 

240 

Linen  Towels,  in  cases    

40 

6 

240 

Sisal,  compressed      

21 

8 

168 

Tow,  compressed      

29 

8 

232 

Wool,  in  bales,  compressed     .    .    . 

48 

Wool,  in  bales,  not  compressed 

13 

8 

104 

Wool,  Worsted,  in  cases      .... 

27 

8 

216 

49 


CORRUGATED      BAR      COMPANY,     INC. 


CONTENTS  OF  STORAGE  WAREHOUSES 


Material 

Weights 
per 
Cubic  Foot 
of  Space, 
Pounds 

Height 
of  Pile, 
Feet 

Weights 
per 
Square  Foot 
of  Floor, 
Pounds 

Recom- 
mended 
Live  Loads, 
Pounds  per 
Square  Foot 

BUILDING  MATERIALS 

Cement,  Natural  

59 

6 

354 

300  to  400 

Cement,  Portland     

73 

6 

438 

Lime  and  Plaster 

53 

5 

265 

HARDWARE,  ETC. 

Door  Checks 

4^ 

Hinges 

TTtJ 

64 

Locks,  in  cases,    packed  

31 

Sash  Fasteners       

48 

Screws     .    .                   ... 

101 

Sheet  Tin,  in  boxes    

278 

2 

556 

300  to  400 

Wire  Cables,  on  reels    

425 

Wire,  Insulated  Copper,    in  coils    . 

63 

5 

315 

Wire,  Galvanized  Iron,   in  coils 

74 

43^ 

333 

Wire,  Magnet,  on  spools      .... 

75 

6 

450 

DRUGS,  PAINTS,  OIL,  ETC. 

Alum,  Pearl,  in  barrels     

33 

6 

198 

Bleaching  Powder,  in  hogsheads 

31 

3$i 

102 

Blue  Vitriol,  in  barrels     

45 

5 

226 

Glycerine  in  cases 

en 

Q-J2 

Linseed  Oil,  in  barrels       

36 

_ 

6 

216 

Linseed  Oil,  in  iron  drums       .    .    . 

45 

4 

180 

Logwood  Extract,  in  boxes      .    .    . 

70 

5 

350 

Rosin,  in  barrels 

48 

ft 

288 

200  to  300 

Shellac,  Gum      

38 

\J 

ft, 

^-fOO 

228 

&\J\J  L(J  O\J\J 

Soda  Ash,  in  hogsheads    

62 

2% 

167 

Soda,  Caustic,  in  iron  drums     .    .    . 

88 

31^ 

294 

Soda,  Silicate,  in  barrels       .... 

53 

6 

318 

Sulphuric  Acid       

60 

1% 

100 

White  Lead  Paste,  in  cans       .    .    . 

174 

31^ 

610 

White  Lead,  dry    

86 

4M 

408 

Red  Lead  and  Litharge,  dry    .    .    . 

132 

3% 

495 

MISCELLANEOUS 

Glass  and  Chinaware,  in  crates 

40 

8 

320 

Hides  and  Leather,  in  bales     .    .    . 

20 

8 

160 

Hides,  in  bundles       

37 

8 

296 

Paper,  Newspaper  and  Strawboards 

35 

6 

210 

300 

Paper,  Writing  and  Calendered 

60 

6 

360 

Rope,  in  coils      

32 

6 

192 

50 


USEFUL      DATA 


BUILDING  CODE  REQUIREMENTS  FOR  LIVE  LOAD 


Structure 

Baltimore 

! 
1 

| 

1 

'"§ 

1 

Milwaukee 

i 

Apartments     

60 

50 

70 

40 

40 

50 

30 

50 

Public  Rooms  and  Halls           .... 

100 

100 

Assembly  Halls 

100 

100 

100 

125 

125 

Fxd.  Seat  Auditoriums      

75 

100 

50 

Mov.  Seat  Auditoriums 

125 

80 

Churches 

100 

100 

125 

KO 

Dance  Halls    .    .       

200 

100 

150 

100 

Drill  Rooms 

200 

100 

Theaters  

100 

100 

100 

125 

50 

Theater  Balconies 

Theater  Stairways      

80 

Dwellings     

60 

50 

40 

40 

40 

50 

30 

50 

Hospitals 

70 

KA 

K/) 

QA 

K.f) 

Hotels  

60 

70 

50 

40 

75 

30 

50 

First  Floors                                       .     . 

100 

Corridors     

Office  Rooms 

50 

Manufacturing   
Light  Manufacturing     
Mercantile 

175 
125 
125 

125 
2^0 

120 

100 
100 

150 
100 

200 
100 

100 

100 

Retail  Stores  

125 

125 

120 

100 

100 

100 

100 

100 

Heavy  Storehouses 

250 

2^)0 

1^0 

200 

"Warehouses 

2^0 

1  ^0 

ICA 

900 

Offices  

75 

100 

70 

50 

50 

7*. 

40 

75 

First  Floor 

IK/) 

100 

1  W 

on 

100 

Corridors     

Public  Buildings     
Schools  —  Class  Rooms  
Assembly  Rooms    

75 

60 
IOK. 

100 

7K 

100 
60 

100 

40 
60 

100 

Corridors     ...        .... 

fiO 

Stairways 

fiO 

Sidewalks     . 

200 

QflO 

QAA 

1^0 

300 

Stables,  Carriage  Houses,  Garages      .     . 
Stairways  General 

100 

70 

120 

100 
100 

75 

on 

85 

80 
fio 

85 

Fire  Escapes   .           ........ 

7O 

R00fs  —  Slope  Under  20° 

40 

Aft 

OK 

OK 

Oft 

on 

Cft 

Over  20°  (Hor.  Proj.)    

tjO 

Wind  Pressures       

QA 

OA 

20 

90 

OA 

on 

51 


CORRUGATED   BAR   COMPANY,  INC. 


BUILDING  CODE  REQUIREMENTS  FOR  LIVE  LOAD 


Structure 

New  Orleans 

1 
1 

Philadelphia 

Pittsburgh 

St.  Louis 

1 

Seattle 

Washington 

Apartments     

40 

40 

,50 

60 

40 

50 

Public  Rooms  and  Halls  

70 

75 

Assembly  Halls              .       .... 

100 

100 

150 

100 

Fxd.  Seat  Auditoriums 

75 

75 

Mov.  Seat  Auditoriums     

125 

100 

Churches 

75 

75 

Dance  Halls 

150 

100 

Drill  Rooms       

150 

950 

Theaters 

100 

75 

75 

Theater  Balconies  

Theater  Stairways 

100 

Dwellings    

40 

40 

40 

70 

50 

60 

40 

50 

Hospitals         

40 

50 

60 

50 

Hotels 

40 

40 

50 

60 

40 

50 

First  Floors     

100 

75 

Corridors 

1?5 

100 

75 

Office  Rooms  

75 

Manufacturing                  

150 

?00 

150 

?50 

Light  Manufacturing 

1?5 

190 

100 

1?5 

195 

Mercantile       

?00 

150 

Retail  Stores 

1?5 

1?0 

1?0 

150 

195 

195* 

110 

Heavy  Storehouses    

150 

250 

150 

Warehouses        .       .    . 

?00 

150 

900 

150 

?50 

150 

Offices 

70 

60 

60 

60 

60 

50 

75 

First  Floor          

100 

195 

Corridors 

100 

110 

Public  Buildings     

135 

100 

100 

110 

Schools  —  Class  Rooms                         . 

60 

75 

75 

75 

75 

50 

75 

Assembly  Rooms 

T>5 

75 

Corridors                        

195 

100 

Stairways 

Sidewalks    .    .           

300 

300 

150 

Stables,  Carriage  Houses,  Garages      .    . 
Stairways,  General    

70 

100 

75 

75 

100 

Fire  Escapes                  ....        . 

70 

100 

Roofs  —  Slope  under  20° 

30 

40 

30 

50 

30 

30 

40 

95 

Over  20°  (Hor.  Proj.)    

30 

90 

40 

95 

^^ind  Pressures 

30 

30 

30 

90 

30 

USEFUL      DATA 


WEIGHTS  OF  MATERIAL 


Substance 

Weight, 
Pounds 
per 
Cubic  Foot 

Substance 

Weight, 
Pounds 
per 
Cubic  Foot 

ASHLAR  MASONRY 
Granite,  syenite,  gneiss  .    .    . 
Limestone,  marble   

165 

160 

EARTH,  ETC.,  EXCAVATED. 
(CONTINUED) 

Earth,  dry,  loose  

76 

Sandstone,  bluestone  .... 

MORTAR  RUBBLE  MASONRY 
Granite,  syenite,  gneiss  .    .    . 
Limestone,  marble  
Sandstone,  bluestone  .... 

140 

155 
150 
130 

Earth,  dry,  packed  
Earth,  moist,  loose  
Earth,  moist,  packed       .    .    . 
Earth,  mud,  flowing    .... 
Earth,  mud,  packed    .... 
Riprap,  limestone 

95 
78 
96 
108 
115 
80-115 

DRY  RUBBLE  MASONRY 
Granite,  syenite,  gneiss  .    .    . 
Limestone,  marble   
Sandstone,  bluestone  .... 

BRICK  MASONRY 
Pressed  brick        .    . 

130 
125 
110 

140 

Riprap,  sandstone    
Riprap,  shale    
Sand,  gravel,  dry,  loose  .    .    . 
Sand,  gravel,  dry,  packed  .    . 
Sand,  gravel,  dry,  wet     .    .    . 

EXCAVATION  IN  WATER 

90 
105 
90-105 
100-120 
118-120 

Common  brick 

120 

Sand  or  gravel 

60 

Soft  brick  

100 

Sand  or  gravel  and  clay     .    . 

65 

Clay 

80 

CONCRETE  MASONRY 

River  mud 

90 

Cement,  stone,  sand    .... 

144 

Soil     

70 

Cement,  slag,  etc  

130 

Stone  riprap 

65 

Cement,  cinder,  etc  

VARIOUS  BUILDING  MATERIALS 
Ashes,  cinders  .    . 

100 
40-45 

MINERALS 
Asbestos    

153 

Cement,  Portland,  loose     .    . 

90 

ICQ 

Barytes  
Basalt 

281 
184 

Lime  gypsum  loose 

53-64 

Bauxite          

159 

JVIortar  set 

103 

Borax     

109 

Slags,  bank  slag    .    . 

67-72 

Chalk     

137 

Slags  bank  screenings 

98-117 

Clay,  marl                

137 

Qfi 

Dolomite 

181 

Slags,  slag  sand 

49-55 

Feldspar,  orthoclase    .... 

159 

Gneiss  serpentine        .... 

159 

EARTH,  ETC.,  EXCAVATED 

Granite  syenite 

175 

Clay,  dry  

63 

Greenstone,  trap  

187 

Clay,  damp,  plastic    .... 

110 

Gypsum,  alabaster  

159 

Clay  and  gravel,  dry 

100 

Hornblende              

187 

53 


CORRUGATED      BAR      COMPANY,     INC. 


WEIGHTS  OF  MATERIAL 


Substance 

Weight, 
Pounds 
per 
Cubic  Foot 

Substance 

Weight, 
Pounds 
per 
Cubic  Foot 

MINERALS  —  CONTINUED 
Limestone,  marble       .... 

165 

COAL,  PILED  —  CONTINUED 
Coal,  peat  turf 

9fl_9A 

M^agnesite 

187 

Coal  charcoal 

6\J-&\) 
1fL-1  A 

Phosphate  rock,  apatite  .    .    . 
Porphyry 

200 

172 

Coal,  coke     

IU—  14 

23-32 

Pumice,  natural    

40 

Quartz,  flint  
Sandstone,  bluestone  .... 
Shale  slate           

165 
147 
175 

Soapstone  talc 

169 

METALS,  ALLOYS,  ORES 

STONE,  QUARRIED,  PILED 

Qfi 

Aluminum,  cast-hammered     . 
Aluminum,  bronze   
Brass,  cast-rolled 

165 
481 
534 

Limestone,  marble,  quartz      . 
Sandstone                 

95 

82 

Bronze,  7.9  to  14%  Sn    .    .    . 
Copper,  cast-rolled  

509 
556 

Shale      

92 

Copper,  ore  pyrites  

262 

Greenstone,  hornblende  .    .    . 
BITUMINOUS  SUBSTANCES 

107 

Gold,  cast-hammered  .... 
Iron,  cast,  pig  
Iron,  wrought 

1205 
450 

485 

Asphaltum            

81 

Iron,  steel  

490 

Coal  anthracite 

Q7 

Iron,  speigel-eisen            .    .    . 

468 

Coal,  bituminous      
Coal   lignite 

84 

78 

Iron,  ferro-silicon     
Iron,  ore,  hematite           .    .    . 

437 
325 

Coal,  peat,  turf,  dry    .... 

47 

Iron,  ore  limonite     

237 

Coal,  charcoal,  pine     .... 
Coal,  charcoal,  oak  

23 
33 

Iron,  ore  magnetite      .... 
Iron,  slag  

315 

172 

Coal  coke         

75 

Lead       .    .           

710 

Graphite 

Lead   ore  galena 

465 

Paraffine                   

56 

Manganese    

475 

Petroleum 

54 

Manganese  ore,  pyrolusite 

259 

Petroleum  refined    

50 

Mercury     

849 

Petroleum  benzine 

46 

Nickel 

565 

Petroleum  gasoline  
Pitch 

42 
69 

Nickel  monel  metal      .... 
Platinum,  cast-hammered 

556 
1330 

Tar,  bituminous  

COAL  AND  COKE,  PILED 
Coal  anthracite 

75 
47-58 

Silver,  cast-hammered     .    .    . 
Tin,  cast-hammered     .... 
Tin,  ore,  cassiterite  
Zinc,  cast-rolled    

656 
459 
418 
440 

Coal  bituminous  lignite 

50-54 

Zinc  ore  blende 

253 

54 


USEFUL      DATA 


WEIGHTS  OF  MATERIAL 


Substance 

Weight, 
Pounds 
per 
Cubic  Foot 

Substance 

Weight, 
Pounds 
per 
Cubic  Foot 

VARIOUS  SOLIDS 
Cereal,  oats,  bulk  

32 

TIMBER  —  CONTINUED 
Maple,  hard  .... 

43 

Cereal,  barley,  bulk     .... 

39 

Maple,  white 

33 

Cereal,  corn,  rye,  bulk    .    .    . 

48 

Oak,  chestnut  

54 

Cereal,  wheat,  bulk     .... 
Hay  and  Straw,  bales      .    .    . 

48 
20 

Oak,  live    
Oak,  red,  black     

59 
41 

Cotton,  Flax,  Hemp    .... 

93 

Oak,  white 

46 

Fats    
Flour,  loose   

58 
28 

Pine,  Oregon     
Pine,  red    .... 

32 
30 

Flour,  pressed       
Glass,  common                 .    . 

47 
156 

Pine,  white    
Pine  yellow  long-leaf 

26 
44 

Glass,  plate  or  crown  .... 
Glass,  crystal    

161 

184 

Pine,  yellow,  short-leaf  .    .    . 
Poplar    

38 
30 

Leather  
Paper      
Potatoes,  piled      

59 

58 
42 

Redwood,  California    .... 
Spruce,  white,  black    .       .    . 
Walnut,  black 

26 
27 
38 

Rubber,  caoutchouc     .... 
Rubber,  goods 

59 
94 

Walnut,  white  
Moisture  Contents* 

26 

Salt,  granulated,  piled     .    .    . 
Saltpeter    

48 
67 

Seasoned  timber  15  to  20% 
Green  timber  up  to  50% 

Starch 

96 

Sulphur  

125 

Wool  .    .    . 

82 

VARIOUS  LIQUIDS 

Alcohol,  100%  

49 

Acids,  muriatic  40%    .... 
Acids,  nitric  91%     
Acids,  sulphuric  87%  .... 
Lye,  Soda,  66%    

75 
94 
112 
106 

TIMBER,  U.  S.  SEASONED 

Oils,  vegetable  . 

58 

Ash,  white-red  

40 

K7 

Cedar,  white-red  
Chestnut    

22 
41 

Water,  4°C,  max.  density  .    . 
Water  100°C 

62.428 
59  830 

Cypress  .    . 

30 

\Vn  tf»r    i™» 

Iffi 

Elm,  White   
Fir,  Douglas  spruce     .... 

45 
32 

Water,  snow,  fresh  fallen    .    . 
Water,  sea  water  

8 
64 

Fir,  eastern   
Hemlock    

25 
29 

Hickory     ... 

49 

GASES,  Ara  =  l 

Locust    

46 

Air  0°C  760  mm 

0807 

55 


CORRUGATED   BAR   COMPANY,  INC. 


WEIGHTS  OF  BUILDING  MATERIALS 


Kind 

Weight  in  Ib. 
per  sq.  ft. 

FLOORS 
%"  Maple  finish  floor  and  %"  Spruce  under  floor  on  2"  x  4"  sleepers,  16"  centers, 
with  2"  dry  cinder  concrete  filling  
Cinder  concrete  filling  per  inch  of  thickness 

18 
7 
12 
18 
21 
23 

5 

10 

6 

5H 

16 

9^ 

12 
20 
6 

Asphalt  mastic  flooring  1H"  thick      

3"  creosoted  wood  blocks  on  J^"  mortar  base           

Solid  flat  tile  on  1"  mortar  bed 

CEILINGS 
Plaster  on  tile  or  concrete                .                   .        

Suspended  Metal  Lath  and  plaster 

ROOFS 
Five-ply  felt  and  gravel                           

Four-ply  felt  and  gravel 

Three-ply  ready  roofing    .        

Cement  Tile                                                          

Slate   }4"  thick 

Sheathing  I"  thick  Yellow  Pine 

2"  Book  Tile                                                                

3"  Book  Tile                                                                                                        .    . 

Kind 

WEIGHT  IN  LB.  PER  SQ.  FT. 

Unplastered 

One  Side 
Plastered 

Both  Sides 
Plastered 

WALLS 
9"  Brick  Wall   

84 
121 
168 
205 
243 
60 
75 
102 
33 
45 

17 
18 
25 
31 
35 
10 
12 
14 
16 

89 
126 
173 
210 
248 
65 
80 
107 
38 
50 

22 
23 
30 
36 
40 
15 
17 
19 
21 

43 
55 

27 
28 
35 
41 
45 
20 
22 
24 
26 
20 
32 
22 

13"  Brick  Wall   .            
18"  Brick  Wall 

22"  Brick  Wall 

26"  Brick  Wall                                    

4"  Brick  4"  Tile  Backing 

4"  Brick,  8"  Tile  Backing  

9"  Brick  4"  Tile  Backing                    

8"  Tile 

12"  Tile                                       

PARTITIONS 
3"  Clay  Tile                         

4"  Clay  Tile 

6"  Clay  Tile              

8"  Clay  Tile 

10"  Clay  Tile      

3"  Gypsum  Block                

4"  Gypsum  Block    

6"  Gypsum  Block    

2"  Solid  Plaster 

4"  Solid  Plaster        

4"  Hollow  Plaster     . 

MASONRY 


Kind 

Weight  in  Ib. 
per  cu.  ft. 

Kind 

Weight  in  Ib. 
per  cu.  ft. 

Concrete,  cinder  

110 

Mortar  rubble,  sandstone    .    .    . 

130 

Concrete,  stone 

140  to  150 

Mortar  rubble,  limestone    .    .    . 

150 

Concrete,  reinforced  stone     .    . 
Brick  masonry,  soft     

150 
100 

Mortar  rubble,  granite     .... 
Ashlar  sandstone      

155 
140 

Brick  masonry,  common     .    .    . 

125 

Ashlar  limestone   

160 

Brick  masonry,  pressed  .... 

140 

Ashlar  granite      

165 

56 


USEFUL.      DATA 


FLOORS  AND  ROOFS— WITH  EXPLANATION 
OF  TABLES 

Types.  The  selection  of  the  best  type  of  floor  and  roof  construction  depends  upon 
the  spans,  loads  to  be  carried,  character  of  the  building  and  local  conditions.  Build- 
ings readily  divide  themselves  into  two  general  groups, — those  primarily  for  the 
housing  of  people,  and  those  for  warehousing  and  industrial  purposes. 

In  structures  of  the  first  group,  comprising  office  and  public  buildings,  schools, 
hospitals,  hotels,  apartments,  dwellings  and  garages  the  majority  of  the  spans  are 
long  and  the  loads  light  (40  to  125  pounds  per  square  foot).  Such  conditions  require  a 
greater  depth  of  slab,  to  avoid  undue  deflection,  than  would  be  demanded  for  strength 
alone,  and  the  problem  is  usually  solved  through  the  use  of  a  concrete  ribbed  floor 
employing  clay  or  composition  tile,  metal  or  wood  forms  of  whatever  depth  may  be 
necessary.  In  the  case  of  clay  or  composition  tile  they  always  remain  a  part  of  the 
permanent  floor  and  may  be  said  to  represent  the  best  type  of  form  or  filler  for  con- 
crete ribbed  slabs;  they  add  stiffness  and  strength  to  the  construction  and  in  no  way 
detract  from  its  fireproof  ness.  To  reduce  the  cost,  however,  metal  forms  are  frequently 
used  and  may  be  of  either  the  removable  or  permanent  type.  Permanent  metal 
forms  are  of  light  gauge  steel  sheets,  stiffened  transversely  by  corrugations,  to  enable 
them  to  withstand  the  loads  and  impacts  of  service;  they  add  nothing  to  the  struc- 
tural efficiency  of  the  floor  and,  in  fact,  may  damage  the  concrete  through  expansion 
of  the  exposed  metal  in  case  of  fire.  For  this  reason,  if  metal  forms  are  used,  those  of 
a  removable  type  would  seem  the  proper  selection. 

For  buildings  in  the  warehouse  and  industrial  group  the  loads  usually  vary  from 
125  to  500  pounds  per  square  foot.  Where  the  panels  are  square,  or  approximately  so, 
the  flat  slab  type  of  floor  presents  the  utmost  advantages  structurally  and  economically. 
If,  however,  the  ratio  of  length  of  short  to  long  side  of  panel  exceeds  1 :1M»  a  beam 
and  girder  floor  with  solid  concrete  slabs  should  generally  be  used. 

Treatment.  All  beams,  including  the  ribs  in  concrete  ribbed  slabs,  may  be  classed 
under  one  of  two  types — rectangular  or  T-section.  In  rectangular  beams,  the  con- 
crete above  the  neutral  axis  within  the  limits  of  the  width  of  the  beam  must  resist 
the  total  compressive  stress  (assisted  in  special  cases  by  additional  steel  in  the  com- 
pression area);  whereas,  in  the  T-section  beam  the  flange,  when  built  monolithically 
with  the  web,  materially  increases  the  compressive  resistance  of  the  beam  and  con- 
sequently its  carrying  capacity. 

The  tables  of  safe  loads  for  ribbed  slabs,  continuous  or  partially  continuous,  are 
based  on  a  length  of  span  equal  to  the  distance  center  to  center  of  supports,  with  the 
condition  that  the  tile  or  form,  as  the  case  may  be,  shall  extend  to  within  not  less 
than  twelve  inches  of  the  center  of  support  as  indicated  by  the  illustrations  at  the 
head  of  the  tables.  The  critical  section  for  bending  is  usually  at  this  point  and  as  the 
ratio  between  the  bending  moment  here  and  at  the  center  of  span  varies  with  each 
change  of  span,  it  would  be  uneconomical  to  maintain  a  constant  steel  area  for  each 
fixed  depth  of  slab  on  all  spans.  In  these  tables  the  proper  steel  area  for  each  depth 
and  span  length  is  given. 

Load  and  Moment  Conditions.  The  carrying  capacity  of  beams  and  slabs  is 
dependent  upon  the  condition  of  fixity  at  the  supports  and  the  stresses  allowed  in  the 

57 


CORRUGATED      BAR      COMPANY,     INC. 


steel  and  concrete.  The  safe  load  tables,  pages  61  to  106  inclusive,  have  been  prepared 

rtyt/2  7/1/2 

on  the  basis  of  two  different  stress  combinations  and  for  moments  of  -g-,    JQ  and 

wl* 

TTr*   The  governing  conditions  are  stated  in  the  heading  of  each  table. 

It  is  important  to  note  that  in  the  case  of  ribbed  slabs  or  of  T-beams  continuous 
over  supports,  that  the  critical  compressive  stress  usually  occurs  at  the  supports 
where  the  flange  is  in  tension  and  the  stem  of  the  beam  is  in  compression,  thereby 
resolving  the  problem  into  that  of  a  beam  of  rectangular  section.  However,  as  only  a 
short  section  of  the  beam  is  under  maximum  compression  at  this  point  it  is  considered 
entirely  permissible  to  employ  a  higher  unit  stress  in  the  concrete  here  than  at  the 
center  of  span.  This  feature  has  been  carefully  considered  in  preparing  the  tables  for 
continuous  or  semi-continuous  ribbed  slabs  and  T-beams  and  the  maximum  fibre 
stress  in  the  concrete  at  supports  has  been  held  to  a  value  not  exceeding  15%  greater 
than  the  fibre  stress  noted  in  the  table.  This  is  in  accordance  with  the  recommendations 
of  the  Joint  Committee  on  Concrete  and  Reinforced  Concrete. 

In  the  case  of  T-beams  continuous  over  supports  the  straight  bars  in  the  bottom 
of  the  beam  are  considered  to  act  as  compressive  reinforcement  and  should  be  carried 
past  the  face  of  the  support  a  sufficient  distance  to  develop  their  stress  in  bond. 

Shear.  After  selecting  from  the  tables  the  proper  slab  or  beam  to  be  used  for 
any  particular  load,  special  attention  should  be  given  to  the  shear  reinforcement 
required.  For  the  solid  concrete  slabs  the  loads  given  produce  shears  of  less  than 
forty  pounds  per  square  inch  on  the  area  bjd.  For  the  concrete  ribbed  slabs  loads 
to  the  left  of  the  heavy  stepped  line  produce  shears  in  excess  of  ninety  pounds  per 
square  inch  on  bjd  and  vertical  stirrups  should  be  used  in  addition  to  the  bent  up 
bars  in  the  ribs. 

In  the  case  of  the  beam  tables,  to  satisfy  the  majority  of  code  requirements,  stirrups 
will  have  to  be  provided.  Particular  attention  is  called  to  the  fact  that  all  loads  to 
the  left  of  the  heavy  stepped  line  produce  shears  in  excess  of  120  pounds  per  square 
inch  on  bjd. 

Fireproofing.  In  preparing  the  tables  the  depth  of  fireproofing  under  the  rein- 
forcement was  taken  at  %  in-  f°r  solid  and  ribbed  slabs  and  1%  m-  f°r  beams.  As  the 
fireproofing  determines  the  effective  depth  for  any  given  slab  or  beam  it  will  be  nec- 
essary to  increase  or  reduce  the  table  load  should  a  change  be  made  in  the  amount  of 
fireproofing.  This  may  be  effected  by  multiplying  the  sum  of  the  superimposed  and 
dead  loads  of  the  table  by  the  square  of  the  ratio  of  the  new  effective  depth  to  the 
given  effective  depth.  This  gives  the  new  total  load  from  which  should  be  deducted 
the  dead  load  in  order  to  obtain  the  new  superimposed  load. 

The  following  examples  illustrate  the  use  of  the  tables: 

Solid  Concrete  Slabs.  Given  a  floor  layout  consisting  of  solid  concrete  slabs, 
continuous  over  beams  spaced  12'-0"  in  the  clear.  The  floor  to  carry  a  live  load  of  150 
pounds  per  square  foot,  a  wood  finish  on  sleepers  embedded  in  2  inches  of  cinder 
concrete  and  a  plastered  ceiling;  the  finish  and  plaster  weighing  together  25  pounds 
per  square  foot,  giving  a  total  superimposed  load  of  175  pounds  per  square  foot.  The 
stress  in  the  steel  not  to  exceed  16,000  pounds  per  square  inch  and  in  the  concrete 
650  pounds  per  square  inch. 

58 


USEFUL      DATA 


The  table  on  page  63  for  slabs  continuous  over  supports  and  based  on  the  specified 
unit  stresses  shows  that  a  6^-inch  slab  reinforced  with  Y%  round  bars,  7^  inches  on 
centers,  will  carry  178  pounds  per  square  foot. 

Concrete  Ribbed  Slabs— Clay  Tile  Fillers:  Given  a  floor  of  22'-0"  span,  non- 
continuous.  This  floor  is  to  carry  a  live  load  of  70  pounds  per  square  foot,  a  wood 
floor  on  cinder  concrete  fill  and  a  plastered  ceiling;  the  finish  and  plaster  weighing 
together  27  pounds  per  square  foot,  thus  giving  a  total  superimposed  load  of  97  pounds 
per  square  foot.  Steel  stress  16,000  pounds  per  square  inch  and  concrete  650  pounds 
per  square  inch. 

The  table  on  page  67  for  non-continuous  slabs  shows  that  a  10"+2^"  slab  with 
1.15  square  inches  of  steel  in  each  rib  will  carry  106  pounds  per  square  foot  and  a 
12"+2"  slab  with  1.04  square  inches  of  steel  will  carry  112  pounds  per  square  foot. 
If  the  10" +2W  slab  is  selected  the  area  of  steel  called  for  in  the  table  may  be  reduced 
in  the  ratio  of  actual  total  load  per  square  foot  to  the  total  carrying  capacity  per 
square  foot  or, 

New  steel  area  =  (1.15)   L  -j  =1.10  sq.  in.  per  rib. 

This  area  may  be  secured  by  using  1*4"  rounds  and  \l/%  rounds  in  alternate  ribs 
or  2-%"  squares  in  each  rib.  If  the  12"-|-2"slab  is  used  the  table  area  of  1.04  square 
inches  may  be  similarly  reduced  to  0.96  square  inch  and  a  \Y%  round  bar  placed  in 
each  rib. 

Concrete  Ribbed  Slabs— Steel  or  Wood  Forms.  Consider  a  floor  slab  of  21 '-0" 
span  continuous  on  one  end  only.  The  floor  is  to  carry  a  live  load  of  80  pounds  per 
square  foot,  a  wood  floor  on  cinder  concrete  fill  weighing  18  pounds  per  square  foot 
and  a  ceiling  of  plaster  on  metal  lath  weighing  10  pounds  per  square  foot,  giving  a 
total  superimposed  load  of  108  pounds  per  square  foot. 

The  table  on  page  74  gives  for  a  12"+3"  slab  reinforced  with  1.30  square  inches  of 
steel  in  each  rib  a  carrying  capacity  of  122  pounds  per  square  foot.  As  this  is  in  excess 
of  the  requirements  the  table  area  of  steel  may  be  reduced  as  in  the  previous  example 
arid  an  area  of  1.20  square  inches  used.  This  area  is  secured  by  using  2- J^"  round  bars 
in  each  rib. 

Tee-Beams, — Continuous  over  supports.  Determine  size  and  reinforcement  of 
a  beam  in  a  floor  construction  assuming  the  span  to  be  22  feet,  the  superimposed  load 
200  pounds  per  square  foot,  the  floor  slab  4}/£"  thick  and  the  distance  center  to  center 
of  beams  as  7'-0".  The  beam  is  continuous  over  supports  and  the  unit  stresses  employed 
are  to  be  as  follows:  /8,  16,000;  /c,  650;  and  v,  120.  Haunches  are  not  to  be  used  at  the 
ends  of  the  beams.  This  represents  the  type  of  beam  usually  encountered  in  building 
construction  commonly  referred  to  as  a  T-beam,  but  due  to  the  continuity  at  supports 
its  capacity  must  necessarily  be  rated  on  the  section  of  the  web  of  the  beam  rather 
than  upon  the  T-section  at  center  of  span. 

From  the  data  given  the  total  load  per  square  foot  of  floor,  including  the 
Weight  of  the  slab,  is  found  to  be  256  pounds  per  square  foot,  or  1,792  pounds 
per  linear  foot  of  beam.  By  referring  to  the  table  on  page  98  it  will  be  found  that 
a  10"  x  26"  beam  reinforced  with  4-1"  round  bars  will  carry,  exclusive  of  the 
weight  of  beam,  1,927  pounds,  which  from  a  practical  standpoint  fulfills  the  conditions 
of  the  problem. 

59 


CORRUGATED      BAR      COMPANY,     INC. 


If  it  is  required  to  maintain  a  minimum  depth  of  beam  it  will  be  found  that  a  14"  x  22" 
beam,  reinforced  with  6-%*  round  bars  will  carry  the  load.  It  will  be  noted,  however, 
that  the  shallower  beam  requires  more  steel  and  concrete. 

To  determine  the  number  of  stirrups  required  for  the  10"  x  26"  beam,  find  the  end 
shear. 


(2,062)  (^ 

=  113  Ib.  per  sq.  in. 


(0(10)  (23) 


From  the  table  on  page  107  for  an  end  shear  of  120  pounds  per  square  inch  a  10-inch 
beam  of  22  foot  span  requires  20-%*  round  stirrups,  and  for  an  end  shear  of  100  pounds 
per  square  inch,  14-%*  round  stirrups.  As  the  actual  end  shear  is  113  pounds  per  square 
inch,  by  interpolation,  18-%"  round  stirrups  will  be  sufficient. 

In  the  tables  which  follow  the  endeavor  has  been  made  to  give  a  fairly  wide  range  of 
values  from  which  to  make  the  desired  selection  of  size  of  member  and  reinforcement 
required,  so  that  knowing  the  load  and  span  the  designer  may  enter  the  tables 
and  choose  the  beam  or  slab  which  best  meets  the  needs  of  his  particular  case, 
much  as  he  would  select  a  beam  from  a  safe  load  table  in  a  structural  steel  hand- 
book. 


60 


USEFUL      DATA 


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61 


CORRUGATED      BAR      COMPANY,     INC. 


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62 


USEFUL      DATA 


Solid 

Concrete 

Slabs 


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107 


CORRUGATED   BAR   COMPANY,  INC. 


FLAT  SLAB  TABLES 

CORK-PLATE   FLOORS 

(PATENTED) 

Flat  slab  floors,  or  floors  in  which  beam  elements  are  omitted  and  the  slab 
supported  directly  on  the  columns,  are  the  result  of  the  ever-present  demand  for 
efficiency  and  economy  of  construction,  particularly  for  buildings  in  the  warehouse 
and  industrial  group.  This  demand  has  been  met  by  numerous  "systems"  of  flat 
slab  floors,  each  reflecting  the  ideas  of  the  designer  as  to  the  distribution  of  the 
reinforcement;  some  approaching  the  ideal  distribution  and  still  others  varying  widely 
from  the  mark. 

The  Corrugated  Bar  Company,  Inc.,  has  developed  through  its  research  and  labo- 
ratory work,  accompanied  by  field  tests,  a  method  of  design  and  a  system  of  steel 
distribution  which  it  is  believed  meets  the  conditions  of  the  problem  in  the  most 
logical  manner.  This  construction  is  known  as  Corr-Plate — a  flat  slab  reinforced  in 
two  directions  in  such  manner  as  to  conform  to  the  variation  in  moment  that  exists  in 
a  flat  plate  on  point  supports  when  subjected  to  load,  and  for  which  is  claimed  the 
following  engineering  advantages : 

(a)  That  it  can  be  accurately  designed. 

(6)  That  the  arrangement  of  reinforcement  in  two  directions,  parallel  to  the  sides 
of  the  panel,  is  the  best  arrangement  to  meet  the  stress  distribution  as  observed  in 
laboratory  and  field  tests. 

(c)  That  the  steel  distribution  adopted  varies  with  the  bending  moment,  being 
heaviest  at  the  panel  margin  and  gradually  decreasing  toward  mid-panel. 

(d)  That  having  no  more  than  two  layers  of  reinforcement  at  any  one  point  the 
length  of  arm  of  the  moment  couple  at  any  section  is  the  greatest  possible,  thus  afford- 
ing maximum  strength  and  stiffness  for  a  given  thickness  of  concrete. 

(e)  The  factor  of  safety  being  substantially  uniform  throughout,  there  results  a 
saving  in  quantity  of  concrete  and  reinforcement. 

Aside  from  the  specific  advantages  claimed  for  Corr-Plate  Floors,  flat  slab  con- 
struction in  general  appeals  to  the  owner  and  builder  from  the  economic  and  service 
standpoint.  The  advantages  may  be  summed  up  in  the  following  brief  paragraphs: 

(a)  No  beams  or  girders.  This  means  saving  in  forms  and  by  virtue  of  the  flat 
ceiling,  greater  economy  in  the  installation  of  the  sprinkler  system. 

(6)  Saves  space.  From  one  to  one  and  a  half  feet  of  actual  free  space  is  gained  in 
every  story.  This  may  amount  to  a  story  height  in  every  eight,  depending  upon  the 
standard  of  ceiling  heights  used  in  the  building.  The  reduction  in  total  height  of 
building  means  a  saving  in  walls,  columns,  piping,  stairways,  elevator  structure  and 
in  every  item  in  a  building  that  is  affected  by  a  change  in  story  height. 

(c)  Better  light  and  ventilation.   There  are  no  beams  to  cast  shadows  or  interfere 
with  a  thorough  diffusion  of  light.  Flat  ceilings  remove  all  obstacles  to  the  free  move- 
ment of  air  currents  and  to  that  extent  assist  in  maintaining  uniform  conditions  as  to 
temperature,  humidity  and  the  removal  of  vitiated  air. 

(d)  Better  fire  protection.     The  damage  a  concrete  building  sustains  by  fire  bears 
a  direct  relation  to  the  number  of  corners  exposed  to  the  action  of  heat  and  water. 
In  this  respect  it  is  clear  that  the  beamless  floor  has  a  decided  advantage  over  the  beam 

108 


USEFUL      DATA 


and  girder  type  of  construction.  Again,  beams  serve  to  deflect  hose  streams  and  to 
form  pockets  in  the  ceiling  that  collect  and  intensify  heat. 

(e)  Speed  and  economy.  A  flat  slab  building  may  be  erected  in  less  time  and  with 
greater  economy  than  one  of  the  beam  and  girder  type. 

The  moment  factors  used  in  the  design  of  Corr-Plate  Floors,  as  previously  stated, 
are  based  on  the  result  of  experiment  in  the  laboratory  supplemented  by  tests  on 
actual  structures  where  steel  and  concrete  deformations  were  measured  and  stress  and 
moment  distribution  determined  therefrom.  The  distribution  of  moment,  and  sim- 
ilarly of  reinforcement,  is  given  in  Fig.  8,  where,  to  avoid  confusion,  the  distribution 
is  given  for  only  one  set  of  reinforcements.  The  same  methods  are  applied  to  the  rein- 
forcements at  right  angles  to  the  ones  shown.  The  figures  in  the  circles  are  the  denomi- 
nators of  the  moment  coefficient  per  foot  width  of  slab  for  the  band  in  which  they 
appear;  thus  the  positive  moment  per  foot  of  width  at  the  center  of  the  band  extending 

WS2 
between  columns  is,  M=-rrr-and  the  negative  moment  over  the  column  for  the  same 

j  -     ™     WS2 
band  is  M=— 

Similarly  for  the  remaining  bands  into  which  the  panel  is  divided.     The  clear  span 

between  the  column  heads  in  feet,  is  S, 
and  w  is  the  total  dead  and  live  load 
per  square  foot  of  floor.  In  Fig.  8,  the 
heavy  stepped  line  shows  the  practical 
distribution  of  moment  while  the  dashed 
curved  line  shows  the  actual  distribution 
as  determined  by  experiment. 

The  tables  on  pages  110  and  111  are 
based  on  standard  Corr-Plate  design  for 
stresses  of  /8  =  16,000,  /c  =  650;  and/8  = 
18,000,  /c  =  700,  respectively,  and  are  for 
square  interior  panels.  Similar  tables  are 
given  on  pages  112  and  113  to  meet  the 
requirements  of  the.  Chicago  Flat  Slab 
ruling  and  the  Final  Report  of  the  Joint 
Committee.  The  latter  report  is  given 
in  detail  on  pages  194  to  211. 

The  approximate  weight  of  reinforce- 
ment per  square  foot  of  floor  area  is 
given  for  each  span  and  load  and  in- 
cludes steel  required  for  the  support  of 

Distribution  across  Line  Y-  Y  the  negative  moment  reinforcement. 

FIG.  8 


109 


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113 


CORRUGATED      BAR      COMPANY,     INC. 


COLUMN  TABLES 

Concrete  columns  are  usually  reinforced  either  with  vertical  bars  tied  together  at 
intervals  by  steel  hoops  or  with  vertical  bars  and  spiral  hooping.  These  two  general 
types  of  column  are  referred  to  in  the  tables,  pages  115  to  132,  as  "Tied  Columns"  and 
"Spiral  Columns."  These  tables  give  safe  loads  in  thousands  of  pounds  for  columns 
to  meet  the  requirements  of  the  New  York  or  Chicago  building  codes,  or  the  Final 
Report  of  the  Joint  Committee  on  Concrete  and  Reinforced  Concrete. 

In  New  York  City  the  code  recognizes  but  two  concrete  mixes  for  columns,  viz., 
1:  2:  4  and  1:  l/^:  3,  while  Chicago  and  the  Joint  Committee  permit,  in  addition  to 
these  two,  a  1 : 1 :  2  mix.  Where  it  is  desired  to  hold  the  column  size  to  a  minimum  the 
advantage  of  the  richer  mix  is  apparent. 

In  the  matter  of  percentages  of  vertical  and  spiral  reinforcement  it  will  be  recog- 
nized that  it  is  not  practicable  to  give  all  possible  combinations  that  could  be  worked 
out  but  there  is  a  sufficient  range  in  each  table  to  satisfactorily  cover  most  require- 
ments. Consider,  for  example,  the  spiral  columns  based  on  New  York  code  require- 
ments, pages  122  to  124.  For  each  column  there  is  given  five  different  percentages  of 
vertical  steel  and  three  different  percentages  of  spiral  reinforcement  for  each  mix,  thus 
yielding  fifteen  load  variations  for  one  size  of  column.  Similarly  for  the  balance  of  the 
column  tables. 

The  following  formulas  express  the  requirements  for  safe  column  load  for  each  of 
the  three  codes  used: 

TIED   COLUMNS 

New  York P  =  Afc  [I  +  (n  -  1)  p] 

Chicago P  =  Afc  [1  +  (n  -  1)  p] 

Joint  Committee P  =  Af0  [1  +  (n  -  1)  p] 

SPIRAL  COLUMNS 

New  York P  =  fc  (A  -  pA)  +  nfcpA  +  2fBp'  A 

Chicago P  =  Afc  (1  +  2.5  np'}  [1  +  (n  -  1)  p] 

Joint  Committee P  =  Afc  [1  +  (n  -  1)  p] 

In  the  above  formulas  the  values  of  /c  and  n  are  noted  in  the  tables.  In  each  case 
p  represents  the  percentage  of  vertical  steel  and  p'  the  percentage  of  spiral.  The  value 
of  fa  in  the  New  York  formula  is  taken  at  20,000  pounds  per  square  inch. 


114 


USEFUL      DATA 


Square 

Tied 

Columns 


Column 
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SQUARE  TIED  COLUMNS 

SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE  REQUIREMENTS 
Ratio  of  Length  of  Column  to  its  Side,  limited  to  15 


Column 
Size 

Core 
Size 

ROUND  BAR 
TIES 

ROUND  BAR 
VERTICALS 

1:2:4  Concrete 
/c  =  500  Ib.  per  sq.  in. 
n=15 

1:  IK:  3  Concrete 
fo  =  600  Ib.  per  sq.  in. 
n=12 

Size 

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in. 

in. 

in. 

in. 

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CORRUGATED      BAR      COMPANY,     INC. 


Size 


'*.; 


SQUARE  TIED   COLUMNS 
SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 

NEW  YORK  CITY  BUILDING  CODE  REQUIREMENTS 
Ratio  of  Length  of  Column  to  its  Side,  limited  to  15 


Column 
Size 

Core 
Size 

ROUND  BAR 
TIES 

ROUND  BAR 
VERTICALS 

1:  2:4  Concrete 
/c  =  500  Ib.  per  sq.  in. 
n  =  15 

1:1K:3  Concrete 
/c  =  600  Ib.  per  sq.  in. 
n  =  12 

Size 

Spacing 

in. 

in. 

in. 

in. 

No. 

Size 

^ 

11 

4 

% 

140 

165 

is 

12 

4 

1 

150 

174 

20 

16 

y± 

12 

6 

153 

177 

M 

12 

8 

K 

162 

185 

\/ 

12 

8 

IK 

184 

206 

1A 

12 

10 

IK 

197 

219 

y± 

11 

4 

M 

157 

185 

y± 

12 

4 

l 

166 

194 

21 

17 

\/ 

12 

6 

l 

177 

204 

Yi 

12 

8 

1 

188 

215 

Yi 

12 

8 

IK 

200 

226 

y± 

12 

12 

IK 

228 

252 

y* 

11 

4 

M 

174 

206 

12 

6 

T/ 

187 

218 

22 

18 

y± 

12 

6 

1 

195 

226 

M 

12 

8 

I 

206 

236 

M 

12 

8 

\Y^ 

231 

259 

M 

12 

12 

IK 

245 

273 

M 

9 

6 

% 

193 

229 

M 

12 

6 

K 

206 

240 

23 

19 

M 

12 

6 

IK 

222 

256 

M 

12 

10 

l 

235 

268 

M 

12 

10 

250 

282 

M 

12 

12 

IK 

284 

314 

M 

11 

6 

M 

219 

258 

M 

12 

6 

l 

233 

271 

24 

20 

M 

12 

6 

242 

279 

y± 

12 

10 

l 

255 

292 

M 

12 

12 

IK 

284 

319 

M 

12 

16 

IK 

311 

345 

M 

11 

6 

M 

239 

282 

i/ 

12 

6 

l 

254 

296 

25 

21 

M 

12 

8 

i 

265 

306 

B 

12 

12 

l 

286 

327 

12 

14 

IK 

318 

356 

M 

12 

18 

IK 

346 

383 

K 

9 

8 

7^ 

259 

307 

M 

12 

8 

276 

322 

26 

22 

12 

10 

1 

297 

342 

J2 

12 

12 

1 

308 

353 

M 

12 

14 

340 

382 

M 

12 

18 

IK 

367 

409 

y 

9 

10 

y 

286 

338 

YL 

12 

10 

K 

307 

357 

27 

23 

M 

12 

10 

l 

320 

369 

M 

12 

14 

l 

341 

390 

\/ 

12 

16 

IK 

376 

422 

M 

12 

20 

IK 

404 

449 

116 


USEFUL      DATA 

Square 

Column 

Tied 
Columns 

Size            * 

oyUArvl^     llr^JJ    CUljUJyiiNb 

'•  '.<"•  fc*-.l>.'-AO.C)""(i:0'<»  :  <a  A^-'o6'1 

QS| 

fa*  v.  m&g  :  >•:  fci'JMJ 

SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 

.  !t&£$#i 

*,       ;'       .     -    ;•,':>, 

•S                 NEW  YORK  CITY  BUILDING  CODE  REQUIREMENTS 
Ratio  of  Length  of  Column  to  its  Side,  limited  to  15 

Column 
Size 

Core 
Size 

ROUND  BAR 
TIES 

ROUND  BAR 
VERTICALS 

1:  2:4  Concrete 
/c  =  500  Ib.  per  sq.  in. 
n  =  15 

1:  1J^:3  Concrete 
/c  =  6001b.  persq.in. 
n  =  12 

Size 

Spacing 

in. 

in. 

in. 

in. 

No. 

Size 

X 

9 

10 

Ys 

310 

366 

12 

10 

% 

330 

385 

28 

24 

% 

12 

12 

1 

354 

408 

14 

12 

14 

1 

365 

418 

M 

12 

18 

l/^ 

413 

463 

H 

12 

22 

l^i 

441 

490 

8 

9 

12 

H 

338 

399 

12 

12 

8 

363 

423 

29 

25 

M 

12 

12 

i 

378 

437 

/4 

12 

14 

jix 

410 

467 

M 

12 

18 

IL/J 

438 

493 

H 

12 

20 

1M 

484 

537 

J€ 

9 

12 

H 

364 

430 

M 

12 

12 

8 

388 

453 

30 

26 

M 

12 

12 

i 

404 

468 

M 

12 

14 

i^ 

435 

497 

M 

12 

20 

477 

537 

H 

12 

22 

i>l 

527 

584 

M 

9 

12 

% 

390 

462 

J4 

12 

14 

T/ 

424 

493 

31 

27 

M 

12 

14 

1 

441 

510 

M 

12 

16 

476 

542 

i^ 

12 

22 

l^i 

518 

582 

8 

12 

24 

1M 

571 

632 

\/ 

9 

14 

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422 

499 

M 

12 

14 

v% 

451 

526 

32 

28 

M 

12 

14 

i 

469 

543 

M 

12 

16 

1^6 

503 

575 

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12 

24 

ILZ 

559 

628 

H 

12 

26 

1M 

615 

680 

M 

9 

14 

H 

450 

533 

M 

12 

14 

Txj 

479 

560 

33 

29 

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12 

16 

1 

508 

587 

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12 

18 

545 

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587 

662 

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12 

28 

1M 

660 

731 

j^ 

9 

16 

5^ 

484 

572 

M 

12 

16 

T£ 

518 

604 

34 

30 

M 

12 

18 

1 

549 

633 

M 

12 

18 

575 

658 

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24 

\\/ 

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734 

H 

12 

30 

1M 

707 

782 

M 

9 

16 

K 

515 

609 

Ji 

12 

16 

« 

548 

640 

35 

31 

Ji 

12 

18 

i 

579 

670 

M 

12 

20 

iH 

619 

707 

M 

12 

24 

IM 

686 

771 

M 

12 

32 

iM 

755 

835 

117 


Square 

CORRUGATED      BAR      COMPANY,     INC. 

Tied 

<        Column 

Size 

l^                              SQUARE  TIED   COLUMNS 

.<  l:'-:^  ^  •*>•<!  .'.'$•'  ••^'r.v'Kj 

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| 

1$ 
SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 
« 
$                            CHICAGO  BUILDING  CODE  REQUIREMENTS 

.               Ratio  of  Length  of  Column  to  its  Side,  limited  to  12 

Column 
Size 

Core 

Size 

ROUND  BAR 

TIES 

ROUND  BAR 

VERTICALS 

1:2:4 
2,000  Ib.Concrete 
/c  =  400  Ib.  per 
sq.  in.      n  =  15 

1:1^:3 
2,400  Ib.Concrete 
/c  =  4801b.  per 
sq.  in.     n  =  12 

1:  1:2 
2,900  Ib.Concrete 
/c  =  580  Ib.  per 
sq.  in.      n  =  10 

Size 

Spacing 

in. 

in. 

in. 

in. 

No. 

Size 

11 

8 

8 

7 
9 

4 
4 

8 

32 
35 

37 

40 

44 
46 

J4 

7 

4 

% 

39 

45 

53 

12 

9 

H 

9 

4 

% 

42 

48 

56 

Yi 

10 

4 

Ft 

46 

52 

60 

% 

7 

4 

% 

47 

54 

64 

13 

10 

a 

9 
10 

4 
4 

8 

50 
53 

57 
61 

67 
71 

H 

12 

4 

i  8 

58 

65 

74 

% 

7 

4 

2i 

55 

65 

77 

14 

11 

B 

9 
10 

4 
4 

K 

58 
62 

67 
71 

79 

83 

>i 

12 

4 

1 

66 

75 

87 

M 

7 

^ 

64 

76 

90 

14 

9 

8^ 

68 

78 

93 

15 

12 

M 

10 

Ji 

71 

82 

96 

L£ 

12 

1 

75 

86 

100 

M 

13 

1H 

80 

90 

104 

y 

7 

Y 

74 

88 

104 

M 

9 

% 

77 

90 

107 

16 

13 

Ji 

10 

V* 

81 

94 

111 

1^ 

10 

6 

% 

88 

100 

117 

M 

12 

6 

1 

94 

106 

123 

M 

7 

4 

% 

85 

101 

120 

10 

4 

V* 

92 

107 

126 

17 

14 

M 

12 

4 

\ 

96 

111 

130 

/4 

10 

6 

% 

99 

113 

133 

X 

13 

6 

l*i 

112 

125 

145 

H 

7 

4 

y* 

97 

114 

137 

L/ 

10 

4 

TX 

104 

121 

143 

18 

15 

M 

10 

6 

% 

110 

127 

149 

ix 

12 

6 

i 

116 

133 

155 

M 

12 

8 

i 

125 

141 

163 

, 

9 

4 

M 

112 

132 

158 

A 

12 

4 

i 

120 

139 

165 

19 

16 

^ 

10 

6 

123 

142 

167 

JL 

10 

8 

7^ 

129 

148 

174 

ft 

13 

8 

1H 

147 

165 

190 

A 

9 

4 

2€ 

126 

148 

177 

12 

4 

1 

133 

155 

184 

20 

17 

A 

12 

6 

1 

142 

164 

192 

A 

12 

8 

1 

151 

172 

200 

A 

13 

8 

IH: 

160 

181 

209 

A 

9 

4 

M 

139 

165 

197 

A 

10 

6 

% 

150 

174 

207 

21 

18 

A 

12 

6 

1 

156 

179 

213 

A 

12 

8 

l 

165 

189 

221 

A 

15 

8 

itf 

185 

207 

239 

118 


USEFUL      DATA 

Square 

Column        r 

Columns 

!'            Size 

»                                 SQUARE  TIED   COLUMNS 

Hi 

._-.  i^ 
SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 
o'  o                                                                                        i 
giU                             CHICAGO  BUILDING  CODE  REQUIREMENTS 

i 

„],,,              Ratio  of  Length  of  Column  to  its  Side,  limited  to  12 

/Jf 

Column 
Size 

Core 
Size 

ROUND  BAB 
TIES 

rlOUND  BAR 

VERTICALS 

1:2:4 
2,000  Ib.Concrete 
/c  =  4001b.  per 
sq.  in.   n  =  15 

1:1^:3 
2,400  Ib.Concrete 
/c  =  4801b.  per 
sq.  in.   n  =  12 

1:1:2 
2,900  Ib.Concrete 
/c  =  580  Ib.  per 
sq.  in.   n  =  10 

Size 

Spacing 

in. 

in. 

in. 

in. 

No. 

Size 

A 

7 

6 

7^ 

155 

183 

219 

JL 

10 

6 

165 

192 

228 

22 

19 

JL 

13 

6 

IK 

178 

205 

241 

JL 

12 

10 

1 

188 

215 

250 

A 

13 

10 

IK 

200 

226 

261 

A 

9 

6 

H 

175 

206 

246 

A 

12 

6 

l 

186 

217 

257 

23 

20 

A 

13 

6 

IK 

193 

223 

263 

A 

12 

10 

l 

204 

233 

273 

A 

13 

12 

IK 

227 

255 

294 

A 

9 

6 

H 

191 

226 

270 

A 

12 

6 

l 

203 

237 

280 

24 

21 

A 

12 

8 

1 

212 

245 

289 

A 

12 

12 

l 

229 

261 

305 

A 

13 

14 

IK 

254 

285 

328 

A 

7 

8 

% 

207 

245 

294 

A 

10 

8 

% 

221 

258 

306 

25 

22 

A 

12 

10 

l 

238 

274 

322 

A 

12 

12 

l 

246 

282 

330 

A 

13 

14 

IK 

272 

306 

353 

% 

7 

10 

KX 

229 

270 

323 

% 

10 

10 

K 

245 

286 

338 

26 

23 

% 

12 

10 

1 

256 

296 

348 

% 

12 

14 

1 

273 

312 

364 

% 

13 

16 

IK 

301 

338 

390 

Y 

7 

10 

% 

248 

293 

350 

% 

10 

10 

T/' 

264 

308 

365 

27 

24 

% 

12 

12 

1 

283 

326 

383 

Y* 

12 

14 

1 

292 

335 

392 

y» 

13 

18 

IK 

330 

371 

427 

% 

7 

12 

!N» 

271 

320 

382 

% 

10 

12 

7X 

291 

338 

400 

28 

25 

y» 

12 

12 

1 

303 

350 

412 

% 

13 

14 

IK 

328 

374 

435 

H 

13 

18 

IK 

350 

395 

456 

y» 

7 

12 

% 

291 

344 

411 

y% 

10 

12 

T/^ 

311 

362 

430 

29 

26 

y% 

12 

12 

\ 

323 

374 

441 

y* 

13 

14 

1  V 

348 

398 

465 

y» 

13 

20 

IK 

382 

429 

495 

y 

7 

12 

Y 

312 

370 

442 

% 

10 

14 

1/0 

339 

394 

467 

30 

27 

y% 

12 

14 

1 

353 

408 

480 

% 

13 

16 

IK 

381 

434 

506 

H 

13 

22 

IK 

414 

465 

537 

y% 

7 

14 

6A 

338 

399 

477 

y% 

10 

14 

K 

361 

421 

499 

31 

28 

y% 

12 

14 

l 

375 

434 

512 

y& 

13 

16 

IK 

403 

460 

538 

H 

13 

24 

IK 

447 

502 

579 

119 


Square 

Tied 

Columns 


CORRUGATED   BAR   COMPANY,  INC. 


Column 
""  Size"" 


:*:  &-j>;»i>-.t>.»?»:.a :  *.«.*••«••&: 

••    *    •• 


SQUARE  TIED   COLUMNS 

SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 

Ratio  of  Unsupported  Length  of  Column  to  its  Side, 
limited  to  15 


Column 
Size 

Core 
Size 

ROUND  BAR 
TIES 

ROUND  BAR 
VERTICALS 

1:2:4 
2,000  Ib.Concrete 
/c  =  4501b.  per 
sq.  in.    n  =  15 

1:1K:3 
2,500  Ib.Concrete 
/c  =  562.5  Ib.  per 
sq.  in.        n  =  12 

1:1:2 
3,000  Ib.Concrete 
/c  =  6751b.  per 
sq.  in.    n  =  10 

Size 

Spacing 

in. 

in. 

in.           in. 

No. 

Size 

K 

8 

4 

K 

34 

41 

48 

12 

8 

8 

10 

4 

37 

44 

51 

12 

4 

% 

40 

47 

54 

1A 

12 

4 

y% 

44 

51 

58 

\i 

8 

4 

K 

41 

50 

59 

is 

10 

4 

44 

53 

62 

13 

9 

\^ 

12 

4 

M 

48 

56 

65 

M 

12 

4 

T/^ 

52 

60 

69 

8 

12 

4 

1 

56 

65 

74 

VA 

10 

4 

% 

53 

64 

75 

\£ 

12 

4 

% 

56 

67 

78 

14 

10 

M 

12 

% 

60 

71 

82 

i^ 

12 

1 

65 

76 

87 

8 

12 

IK 

70 

81 

92 

y\ 

10 

M 

62 

76 

89 

\y 

12 

8^ 

66 

79 

92 

15 

11 

M 

12 

% 

70 

83 

96 

1^ 

12 

1 

74 

87 

101 

M 

12 

1 

84 

97 

110 

u 

76 

92 

108 

H 

80 

96 

112 

16 

12 

M 

12 

i 

85 

100 

116 

IK 

90 

106 

121 

102 

118 

133 

% 

87 

106 

125 

% 

91 

110 

129 

17 

13 

1A 

12 

6 

% 

99 

117 

136 

6 

i 

106 

124 

143 

8 

i 

116 

134 

152 

4 

H 

103 

125 

147 

4 

i 

108 

130 

151 

18 

14 

K 

12 

6 

H 

111 

133 

154 

6 

IK 

126 

147 

169 

8 

IK 

138 

159 

181 

4 

H 

116 

141 

166 

6 

H 

124 

149 

174 

19 

15 

A 

12 

6 

i 

131 

156 

181 

8 

i 

141 

165 

190 

8 

IK 

151 

176 

200 

4 

l 

135 

163 

192 

6 

138 

166 

195 

20 

16 

A 

12 

8 

K 

145 

174 

202 

8 

IK 

165 

193 

221 

10 

IK 

178 

205 

233 

4 

1 

150 

182 

214 

6 

160 

192 

224 

21 

17 

A 

12 

8 

i 

170 

201 

233 

8 

IK 

180 

212 

243 

12 

IK 

205 

236 

268 

120 


USEFUL      DATA 


Square 

Tied 

Columns 


Column 
Size 


..I 


SQUARE  TIED   COLUMNS 

SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 

Ratio  of  Unsupported  Length  of  Column  to  its  Side, 
limited  to  15 


Column 
Size 

Core 
Size 

ROUND  BAR 
TIES 

ROUND  BAR 
VERTICALS 

1:2:4 
2,000  Ib.Concrete 
/c  =  4501b.  per 
sq.  in.  n  =  15 

2,500  Ib.Concrete 
/c  =  562.5  Ib.  per 
sq.  in.  n  =  12 

1:1:2 
3,000  Ib.Concrete 
/c  =  6751b.  per 

sq  in.  n=>10 

Size 

Spacing 

in. 

in. 

in. 

in. 

No. 

Size 

6 

V* 

169 

204 

241 

6 

1 

175 

211 

247 

22 

18 

A 

12 

8 
8 
12 

k 

185 
208 
221 

221 
243 
256 

257 
278 
291 

g 

t/ 

185 

225 

266 

g 

\V 

200 

240 

280 

23 

19 

A 

12 

10 
10 

12 

IB 

219 
225 
255 

252 
265 
294 

291 
304 
333 

g 

i 

210 

254 

299 

24 

20 

A 

12 

6 
10 
12 

r 

218 
230 
255 

262 
274 
299 

306 
318 
343 

16 

ij| 

280 

324 

367 

g 

1 

228 

277 

326 

g 

i 

238 

287 

336 

25 

21 

A 

12 

12 
14 

i 

258 
286 

306 
334 

355 
382 

18 

iij 

311 

359 

406 

g 

i/ 

248 

302 

356 

10 

/% 

267 

321 

374 

26 

22 

H 

12 

12 
14 

i 

277 
306 

331 
358 

384 
411 

18 

iys 

331 

383 

435 

10 

7/ 

276 

335 

393 

27 

23 

% 

12 

10 
14 
16 

1 

1 

288 
307 
338 

346 
366 
396 

405 
424 
454 

20 

1M 

363 

421 

478 

10 

V* 

297 

361 

425 

12 

/  8 

319 

382 

446 

28 

24 

% 

12 

14 
18 

i 

328 
372 

392 
434 

456 
497 

22 

ijj 

397 

459 

521 

12 

_, 

327 

396 

466 

12 

i 

341 

410 

479 

29 

25 

% 

12 

14 
18 

369 
394 

438 
462 

506 
531 

20 

1M 

436 

503 

571 

12 

i/ 

350 

425 

500 

12 

1 

364 

438 

514 

30 

26 

K 

12 

14 
20 

392 
429 

466 
503 

541 
577 

22 

1M 

474 

547 

620 

14 

V* 

381 

462 

543 

14 

1 

397 

478 

559 

31 

27 

H 

12 

16 
22 

24 

1*1 

428 
466 
514 

508 
545 
593 

588 
625 
671 

121 


Spiral 
Columns 


CORRUGATED      BAR      COMPANY,     INC. 


Column    _ 
"'Diameter'    "  *   j. 

*  .x^-o.  *7..<7.-*tx "      rv 


SPIRAL  COLUMNS 

SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 
NEW  YORK  CITY  BUILDING  CODE  REQUIREMENTS 

Ratio  of  Length  of  Column  to  its  Side  or  Diameter, 
limited  to  15. 


Column 

Core 

ROUND  BAR 

1:2:4  Concrete 

1:1^:3  Concrete 

Diam. 

Diam. 

VERTICALS 

/c  =  5001b.  persq.  in. 

/c  =  600  Ib.  per  sq.  in. 

in. 

in. 

No. 

Size 

71  =  15 

n  =  12 

4 

M 

100 

124 

154 

111 

135 

165 

16 

12 

4 

% 

104 

128 

158 

115 

139 

169 

4 

% 

109 

133 

162 

119 

143 

173 

4 

i 

114 

138 

168 

124 

148 

178 

7 

74 

122 

146 

175 

131 

155 

185 

M"<HJi"p 

&"4>-iM"p 

y&"$-\y*"p 

4 

% 

120 

148 

182 

132 

160 

195 

17 

13 

4 

% 

124 

152 

187 

136 

165 

199 

5 

l 

135 

163 

197 

146 

175 

209 

8 

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141 

169 

204 

152 

180 

215 

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134 

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149 

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139 

173 

213 

154 

188 

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179 

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159 

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191 

231 

170 

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181 

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255 

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151 

199 

238 

168 

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164 

204 
211 

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251 

174 
180 

221 
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261 
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235 

275 

203 

250 

290 

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272 

194 

246 

291 

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182 
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233 
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278 
286 

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252 
259 

297 
304 

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300 

222 

273 

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266 

312 

232 

283 

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257 

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279 

330 

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204 
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264 
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335 

244 

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356 

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240 

300 

352 

259 

319 

371 

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283 

347 

243 

307 

371 

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229 

294 

358 

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10 

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385 

279 

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381 

1  282 

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261 

327 

387 

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338 

398 

298 

364 

424 

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1 

291 

357 

417 

316 

381 

441 

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307 

373 

433 

331 

397 

457 

NOTE — Size  and  pitch  of  spiral  wire  is  given  at  head  of  each  group  of  loads  for  eacn  size  column. 

122 


USEFUL      DATA 


Spiral 
Columns 


SPIRAL  COLUMNS 

SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 
NEW  YORK  CITY  BUILDING  CODK  REQUIREMENTS 

Ratio  of  Length  of  Column  to  its  Side  or  Diameter, 
limited  to  15. 


Column 

Core 

ROUND  BAR 

1:2:4  Concrete 

1:1H:3  Concrete 

Diam. 

Diam. 

VERTICALS 

/o  =  500  Ib.  per  sq.  in. 

/0  =  6001b.  persq.  in. 

in. 

in. 

No. 

Size 

n  =  15 

n  =  12 

8 

- 

275 

344 

419 

305 

374 

449 

24 

20 

10 
10 

y 

281 
292 

350 
361 

426 

437 

311 
321 

380 
390 

455 
466 

12 

I 

316 

385 

461 

344 

413 

488 

12 

1H 

333 

403 

478 

360 

429 

505 

8 

^ 

302 

378 

464 

335 

&"4>-2K"p 
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H"<HK"P 
497 

25 

21 

10 
10 

1 

319 
332 

395 
408 

481 
494 

351 
363 

428 
440 

514 
526 

13 

349 

425 

511 

379 

456 

541 

14 

1H 

375 

451 

537 

404 

480 

566 

9 

M 

332 

419 

516 

368 

455 

552 

26 

22 

10 
10 

1 

346 
359 

433 

446 

530 
543 

382 
394 

468 
481 

566 
578 

13 

395 

481 

579 

427 

514 

611 

15 

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408 

495 

592 

441 

527 

625 

10 

365 

456 

551 

405 

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Ji"4>-iM"p 
591 

00 

10 

V% 

376 

467 

562 

415 

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601 

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394 

486 

581 

433 

524 

619 

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424 

516 

611 

461 

552 

647 

16 

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445 

537 

631 

481 

572 

667 

10 

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395 

496 

606 

438 

^"4>-2^"p 
540 

650 

28 

24 

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12 

l 
l 

419 
430 

520 
531 

630 
641 

461 
471 

562 

572 

673 
683 

14 
15 

1% 

461 
493 

563 
594 

673 

'704 

501 
531 

602 
632 

713 
742 

10 

7/s 

439 

550 

653 

485 

597 

699 

on 

25 

10 

1 

452 

564 

666 

497 

609 

712 

12 

1 

463 

575 

677 

508 

620 

722 

15 

501 

613 

715 

544 

656 

758 

16 

1M 

534 

646 

748 

575 

687 

789 

10 

467 

^"4>-2M"p 

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518 

632 

H"<HH"P 
768 

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26 

10 
12 

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480 
508 

594 
623 

730 
759 

530 
556 

644 
671 

780 
807 

16 

JLX 

536 

651 

787 

583 

697 

833 

17 

1*A 

571 

685 

821 

615 

730 

866 

10 

ft 

502 

631 

H"<HJ4"P 
754 

557 

685 

809 

31 

27 

11 
12 

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521 
544 

649 

672 

773 
796 

575 
596 

703 
725 

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848 

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i  i/c 

585 

714 

837 

636 

764 

887 

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623 

752 

875 

672 

800 

923 

Norn— Size  and  pitch  of  spiral  wire  la  given  at  head  of  each  group  of  loada  for  each  size  column. 

123 


Spiral 
Columns 


CORRUGATED   BAR   COMPANY,  INC. 


Column_ ^ 

f~  'Diameter 


SPIRAL  COLUMNS 

SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 
NEW  YORK  CITY  BUILDING  CODE  REQUIREMENTS 

Ratio  of  Length  of  Column  to  its  Side  or  Diameter, 
limited  to  15. 


Column 

Core 

ROUND  BAR 

1:2:4  Concrete 

1:1^:3  Concrete 

Diam. 

Diam. 

VERTICALS 

/c  =  500  Ib.  per  sq.  in. 

/c  =  600  Ib.  per  sq.  in. 

in. 

in. 

No. 

Size 

n=15 

n  =  12 

10 

7A 

532 

663 

y2"$-iy2"p 

793 

591 

722 

852 

32 

28 

12 

1 

556 

687 

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615 

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876 

669 

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i% 

662 

792 

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714 

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564 

699 

834 

627 

762 

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589 

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735 

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622 

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949 

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1021 

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822 

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744 

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1065 

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851 

1019 

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959 

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860 

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727 

890 

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754 
788 

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1096 
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899 

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887 

1056 

1241 

972 

1141 

1326 

31 

18 

948 

1117 

1302 

1029 

1198 

1383 

NOTE — Size  and  pitch  of  spiral  wire  is  given  at  head  of  each  group  of  loads  for  each  size  column. 

124 


USEFUL      DATA 


Spiral 
Columns 


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CORRUGATED      BAR      COMPANY.     INC. 


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126 


USEFUL      DATA 


Spiral 
Columns 


6  .S 
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127 


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128 


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129 


Spiral 

CORRUGATED      BAR      COMPANY,     INC. 

Columns 

Column 
Diameter"       .   J 

04 

1 

SPIRAL  COLUMNS 

SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 

feitil! 

Ratio  of  Unsupported  Length  of  Column  to  its  Core 
Diameter,  limited  to  10 


Column 
Diam- 
eter 

Core 
Diam- 
eter 

ROUND  SPIRAL 
WIRE 

ROUND  BAR 
VERTICALS 

1:2:4 
2,000  Ib.  Concrete 
/0  =  697.51b.  per 
sq.  in.         n  =  15 

1:1^:3 
2,500  Ib.  Concrete 
/c  =  8721b.  per 
sq.  in.         n  =  12 

1:1:2 
3,000  Ib.Concrete 
/0  =  1,046  Ib.  per 
sq.  in.         n  =  10 

Size 

Pitch 

in. 

in. 

in. 

in. 

No. 

Size 

4 

H 

91 

110 

130 

4 

*A 

96 

116 

135 

16 

12 

M 

1H 

4 

y* 

102 

122 

141 

4 

i 

110 

129 

148 

7 

% 

121 

140 

159 

4 

*A 

110 

133 

155 

17 

13 

A 

2M 

4 

% 

116 

139 

161 

5 

1 

131 

153 

176 

8 

% 

140 

162                       184 

5 

*A 

122 

149                      176 

5 

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129 

155 

182 

18 

14 

A 

2H 

5 

y* 

137 

163 

189 

6 

i 

153 

179                       205 

8 

i 

169 

195 

220 

6 

6A 

141 

172 

202 

6 

H 

149 

180 

210 

19 

15 

TS 

IK 

6 

y* 

159 

189 

219 

7 

177 

207 

237 

9 

i 

192 

222 

251 

7 

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161 

196 

230 

7 

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171 

205 

240 

20 

16 

% 

2H 

7 

7A 

181 

216 

250 

8 

1 

202 

236 

269 

10 

1 

217 

251 

284 

8 

6A 

182 

221 

260 

8 

% 

193 

232 

271 

21 

17 

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2^ 

8 

y* 

205 

244 

282 

8 

i 

220 

258 

297 

11 

i 

243 

281 

319 

8 

6A 

201 

245 

289 

9 

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216 

260 

304 

22 

18 

SA 

2M 

9 

7A 

230 

274 

317 

10 

1 

254 

297 

340 

12 

1 

269                       312 

355 

8 

*A 

232                       281                       330 

10 

*A 

241                       290                       338 

23 

19 

H 

2K 

10 

7A 

256                       305                       353 

11 

1 

282                       330                       378 

11 

iys 

305 

352 

399 

8 

3A 

254 

308 

362 

10 

*A 

262 

316 

370 

24 

20 

*A 

2 

10 

7A 

278 

332 

385 

12 

1 

311 

364 

417 

12 

1H 

335 

388 

441 

130 


USEFUL      DATA 


Spiral 
Columns 


SPIRAL  COLUMNS 

SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 

Ratio  of  Unsupported  Length  of  Column  to  its  Core 
Diameter,  limited  to  10 


Column 
Diam- 

Core 
Diam- 

ROUND SPIRAL 
WIRE 

ROUND  BAR 

1:2:4           1         1:1^:3 
2,000  Ib.  Concrete  2.500  Ib.  Concrete 

1:1:2 

3,000  Ib.Concrete 

eter 

eter 

Size 

Pitch 

VERTICALS 

/„  =  697.5  Ib.  per 

/0  =  8721b.  per 

/c=  1,046  Ib.  per 

in. 

in. 

in. 

in. 

No. 

Size 

sq.  in.      »=15 

sq.  in.        n  =  12 

sq.  in.        n  =  10 

8 

H 

276 

336 

396 

10 

H 

300 

360 

419 

25 

21 

ft 

2M 

10 

1 

318 

377 

436 

13 

l 

341 

400 

459 

14 

IM 

378 

436 

493 

9 

* 

304 

370 

435 

10 

324 

389 

454 

26 

22 

A 

2% 

10 

i 

342 

407 

472 

13 

1  1^ 

391 

455 

519     ' 

15 

ij^ 

411 

475 

538 

10 

3^ 

333 

405 

476 

10 

/k 

348 

420 

491 

27 

23 

ft 

2^ 

11 

1 

374 

445 

516 

13 

l/^ 

416 

486 

556 

16 

iy% 

445 

515 

585 

10 

H 

359 

437 

515 

10 

i 

392 

470 

547 

28 

24 

"IS 

2/^ 

12 

i 

408 

485 

562 

14 

ii/g 

452 

528 

604 

15 

1M 

495 

571 

646 

10 

H 

401 

486 

570 

10 

i 

419 

503 

687 

29 

25 

ft 

2//8 

12 

i 

434 

518 

602 

15 

i/^ 

488 

571 

654 

16 

1M 

534 

616 

698 

10 

2i 

429 

521 

612 

10 

ii 

447 

538 

629 

30 

26 

T¥ 

2^4 

12 

487 

577 

668 

16 

i/^ 

525 

615 

705 

17 

1M 

574 

663 

752 

10 

K 

458 

557 

656 

11 

1 

484 

582 

680 

31 

27 

ft 

2}/8 

12 

516 

614 

711 

18 

i/^ 

574 

671 

767 

19 

1M 

627 

723 

819 

10 

% 

488 

594 

701 

12 

l 

521 

627 

733 

32 

28 

ft 

2 

13 

556 

661 

766 

18 

\y% 

604 

708 

812 

20 

1  14 

669 

773 

875 

11 

K 

525 

639 

753 

13 

i 

560 

674 

787 

33 

29 

}/2 

2% 

14 

597 

710 

821 

18 

1  M 

676 

787 

899 

22 

1>£ 

724 

835 

945 

131 


Spiral 

Columns 


CORRUGATED      BAR      COMPANY,     INC. 


SPIRAL  COLUMNS 

SAFE  AXIAL  LOADS  IN  THOUSANDS  OF  POUNDS 
JOINT  COMMITTEE  RECOMMENDATIONS 

Ratio  of  Unsupported  Length  of  Column  to  its  Core 
Diameter,  limited  to  10 


Column 
Diam- 
eter 

Core 
Diam- 
eter 

ROUND  SPIRAL 
WIRE 

ROUND  BAR 
VERTICALS 

1:2:4 
2,000  Ib.  Concrete 
/c  =  697.5  Ib.  per 
sq.  in.         n  =  15 

1:1K:3 
2,500  Ib.  Concrete 
/c  =  8721b.per 
sq.  in.        n  =  12 

1:1:2 
3,000  Ib.Concrete 
/0  =  1,046  Ib.  per 
sq.  in.         n  =  lO 

Size 

Pitch 

in. 

in. 

in. 

in. 

No. 

Size 

12 

ys 

564 

685 

807 

14 

i 

601 

722 

843 

34 

30 

H 

2y2 

15 

IK 

638 

759 

880 

18 

IK 

708 

828 

947 

23 

IM 

769 

887 

1005 

13 

H 

603 

733 

863 

15 

1 

641 

771 

900 

35 

31 

M 

&A 

15 

IK 

672 

801 

930 

• 

18 

IK 

742 

870 

997 

25 

IX 

826 

952 

1078 

14 

% 

643 

782 

920 

15 

i 

676 

814 

952 

36 

32 

y* 

&A 

16 

IK 

716 

854 

991 

20 

1M 

800 

937 

1073 

26 

1M 

873 

1008 

1142 

14 

M 

679 

826 

974 

15 

IK 

742 

889 

1035 

37 

33 

H 

2M 

16 

1M 

788 

934 

1080 

21 

Ik 

851 

996 

1140 

28 

IK 

932 

1075 

1219 

14 

1 

740 

897 

1053 

15 

IK 

779 

935 

1090 

38 

34 

H 

2M 

16 

1M 

825 

980 

1135 

22 

IK 

897 

1051 

1203 

29 

1M 

981 

1133 

1285 

14 

1 

778 

945 

1110 

15 

IK 

817 

982 

1146 

39 

35 

y* 

2l/s 

16 

1M 

863 

1028 

1192 

24 

IM 

958 

1122 

1283 

31 

IM 

1043 

1205 

1365 

14 

i 

817 

993 

1168 

16 

IK 

865 

1040 

1215 

40 

36 

Hi 

21A 

17 

IM 

914 

1087 

1262 

25 

1M 

1010 

1182 

1353 

33 

1M 

1106 

1276 

1446 

14 

1 

857 

1043 

1228 

16 

IK 

905 

1090 

1274 

41 

37 

M 

2 

18 

IM 

965 

1149 

1333 

26 

IM 

1061 

1243 

1425 

35 

IM 

1169 

1349 

1528 

15 

i 

906 

1102 

1298 

17 

IK 

956 

1151 

1345 

42 

38 

H 

2 

19 

IM 

1019 

1212 

1406 

28 

IM 

1126 

1318 

1509 

37 

IM 

1234 

1424 

1613 

132 


'U8-%"0bars,  9-3  each  way 


USEFUL      DATA 

FOOTING  TABLES 

The  purpose  of  a  footing  is  to  distribute  the  column  load  uniformly  over  the  soil 
so  that  unequal  settlements  may  be  avoided.  To  accomplish  this  one  of  three  general 
types  of  foundation  may  be  used:  (a)  square  spread  footings;  (b)  combined  spread 
footings;  (c)  spread  footings  supported  by  piles.  Tables  covering  these  three  types 

are  given  on  pages  136  to  142.  In  special 
cases  there  may  be  employed  cantilever 
footings  or  a  raft  foundation  extending 
over  the  entire  lot  area.  To  cover  these 
in  tabular  form,  however,  would  be 
difficult. 

In  the  table  for  square  column  foot- 
ings the  method  of  design  outlined  in 
Bulletin  67,  University  of  Illinois,  has 
been  followed  and  its  application  is 
illustrated  in  the  following  problem. 
Problem  —  Given  a  column  load  of 
500,000  pounds.  Design  a  square  spread 
footing,  reinforced  in  two  directions,  for 
an  allowable  soil  pressure  of  6,000 
pounds  per  square  foot;  diameter  of 
column  25  inches;  punching  shear  not 
to  exceed  120  pounds  per  square  inch; 
bond  stress  limited  to  100  pounds 
per  square  inch;  /8  =  16,000  and/c  =  650. 
Approximating  the  weight  of  the 
footing  at  400  pounds  per  square  foot, 
the  net  soil  reaction  will  be  6,000  — 
400  =  5,600  pounds  per  square  foot. 
The  area  of  the  footing  will  be,  500,- 
000-^5,600  =  90.4  sq.  ft.  and  we  will 
use  a  footing  9'  6"  x  9'  6". 


FIG.  9 


The  effective  depth  of  footing  is  found  by  dividing  the  column  load,  less  the  net 
soil  reaction   directly    under  the  column   area,   by   the  perimeter  of  the    column 


multiplied    by   the    unit    punching   shear,   or  Eff.  depth  = 


500,000-19,000 


=51  in. 


(25) (3. 14) (120) 
To  the  effective  depth  should  be  added  3  inches  of  concrete  for  the    protection 

of   the  metal,  giving   a    total   depth   of   footing  of  4'  6". 

The  area  of  steel,  in  one  direction,  to  resist  the  moment  of  the  net  soil  reaction 

about  the  edge  BC  of  the  cap,  is 


(2. 71)  (5,600)  (1.53)  (12) 


~]  (33)  (16,000) 


4.10  sq.  in. 


This  area  is  equivalent  to  14 — %"  round  bars. 

As  it  is  required  to  maintain  the  bond  stress  at   100  pounds  per  square  inch 


133 


CORRUGATED   BAR   COMPANY,  INC. 


(assuming  the  use  of  deformed  bars),  the  number  of  bars  selected  for  moment  consider- 
ations may  not  be  sufficient  to  accomplish  this.   In  this  case  the  unit  bond  stress,  . 


(14)  (1.965)         (33) 


=  130  lb.  per  sq.  in. 


The  allowable  bond  stress  is  exceeded  and  it  will  be  necessary,  therefore,  to  increase 
the  number  of  */%'  round  bars  required  for  moment  in  the  ratio  130/100;  or  a  total 
of  18-^g"  round  bars  will  be  needed  in  each  direction  at  a  uniform  spacing  of  6  inches. 
The  quantities  of  material  required  by  this  design  are:  Concrete  233  cu.  ft.,  steel 
36-%"  round  bars  9'  3"  long. 

The  combined  spread  footing  is  employed  in  those  cases  where  the  footings  under 
wall  columns  are  not  permitted  to  extend  beyond  the  building  line;  this  necessitates 
extending  the  footing  under  the  wall  column  to  the  adjacent  interior  column  and  mak- 
ing it  of  such  dimensions  that  its  center  of  area  coincides  with  the  center  of  gravity 
of  the  column  loads  that  bear  upon  it.  The  footing  thus  becomes  a  distributing  beam, 
uniformly  loaded  by  the  upward  reaction  of  the  soil,  and  is  reinforced  accordingly 
in  the  upper  face  longitudinally  between  columns,  and  in  the  lower  face  transversely 
under  each  column. 

The  designs  given  in  the  tables  on  pages  136  to  139  cover  a  fairly  wide  range  of  con- 
ditions and  as  will  be  noted  it  is  only  required  to  know  the  loads  and  the  distance 
center  to  center  of  the  columns  to  obtain  a  complete  solution  of  the  problem.  Results 
are  all  given  in  terms  of  the  distance  I  in  feet  center  to  center  of  columns.  Where  con- 
ditions depart  from  what  might  be  called  the  average,  the  results  given  in  the  tables 
will  be  slightly  in  error  but  not  sufficiently  so  to  disturb  the  safety  or  economy  of  the 
design. 

Example  —  Given  a  24-inch  square  wall  column  carrying  a  load  PI,  of  350,000 
pounds  and  a  26-inch  diameter  interior  column  carrying  a  load  P2,  of  450,000  pounds, 

or  Py      =1.3.    The  columns  are  spaced  18  feet  on  centers  and  the  allowable  soil 

pressure  is  6,000  pounds  per  square  foot. 

The  sum  of  the  loads  is  800,000  pounds  and  the  distance  c  is  one  foot.    Entering 

the  table  on  page  138  with  Pi+P2  =  800,000  we  find  opposite  the  ratio  P*L  =1.3; 
the  following  dimensions  and  steel  areas: 

L    =  1  .  13J+2c  =  (1  .  13)  (18)  +  (2)  (1)  =  22  .  34  ft. 


H  =( 

h    =3. 6-^=3. 6-^=0. 60ft. 

D  O 

Aa  =27.3sq.  in. 
2,465     2,465 


.„      1,895     1,895      _  or 
A\=  -j-  =Qgiy  =  5.85  sq.  in. 

134 


USEFUL      DATA 


The  disposition  of  the  reinforcing  steel  is  indicated  in  the  cuts  at  the  head  of  the  table. 

Where  soil  conditions  are  of  such  a  nature  that  spread  footings  cannot  be  used, 
resort  must  be  had  to  piles  of  either  wood  or  concrete.  If  the  piles  are  cut  off  below 
the  low  water  line,  wooden  piles  may  be  used,  but  if  exposed  to  alternate  wet  and  dry 
conditions  wood  is  subject  to  rot  and  concrete  piles  should  be  employed.  The  tables  of 
pile  caps  given  on  pages  141  and  142  are  designed  for  concrete  piles  having  an  assumed 
carrying  capacity  of  30  tons  per  pile.  The  style  and  reinforcement  of  cap  and  num- 
ber of  concrete  piles  required  are  determined  from  the  tables,  when  the  column  load  is 
known. 

Designs  for  concrete  piles  of  the  pre-cast  type  are  given  in  the  table  on  page  143. 
Except  under  the  most  adverse  conditions  as  regards  surface  and  sub-soil,  a  load  of 
30  tons  per  pile  may  be  safely  used  and  if  the  piles  are  driven  to  rock  a  50%  increase 
in  load  should  be  permissible.  The  amount  of  reinforcement  used  is  considered  a 
minimum  consistent  with  successful  handling  of  the  pile  from  the  casting  yard  to  its 
place  in  the  work. 


135 


Combined 
Footings 


CORRUGATED   BAR   COMPANY,  INC. 


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136 


USEFUL      DATA 


Combined 
Footings 


CD 


Wi 


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137 


Combined 
Footings 


CORRUGATED      BAR      COMPANY,     INC. 


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138 


USEFUL      DATA 


Combined 
Footings 


ggs  3§88 
% 


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COCOCO<M    cocococo   otfcococo   ^  -tf  co  co 


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139 


CORRUGATED   BAR   COMPANY,  INC. 


1*— 

n 

SQUARE  COLUMN  FOOTINGS 

i 

i 

1 

X, 

•     Unit  Stresses 
/8,  16,000 

|*T=fc=»=B^S=JL- 

.»_•_•_.•_•_•_•_•. 

4! 

/c.       650 

t 

r  

L 

Soil 
Value 

Column 
Load 

Minimum 
Column 
Diameter 

h 

b 

Reinforcement 
Round  Bars 
Each  Way 

Wept 
Steel 

Volume  of 
Concrete 

ft. 

in. 

Ib.  per  sq.  ft. 

in  lOOOlb. 

in. 

ft. 

in. 

ft. 

in. 

No. 

Size 

Ib. 

cu.  ft. 

5 

0 

4000 

96 

13 

0 

7 

i 

10 

14 

H 

88.8 

23.7 

5 

0 

6000 

145 

16 

0 

8 

2 

3 

16 

Yn 

100.3 

29.3 

5 

0 

8000 

194 

18 

0 

10 

2 

7 

15 

y* 

94.1 

38.8 

5 

6 

4000 

116 

14 

0 

8 

2 

1 

14 

y? 

97.0 

33.3 

5 

6 

6000 

175 

17 

0 

10 

2 

6 

15 

Y, 

104.0 

44.4 

5 

6 

8000 

234 

19 

0 

11 

2 

10 

16 

y* 

110.9 

51.6 

6 

0 

4000 

137 

15 

0 

9 

2 

3 

14 

v* 

106.3 

44.5 

6 

0 

6000 

207 

18 

0 

11 

2 

9 

16 

121.4 

58.2 

6 

0 

8000 

278 

20 

1 

0 

2 

11 

18 

IA 

136.6 

65.2 

6 

6 

4000 

161 

16 

0 

9 

2 

4 

17 

y 

140.3 

51.6 

6 

6 

6000 

242 

19 

1 

0 

2 

10 

17 

y% 

140.3 

73.2 

6 

6 

8000 

324 

21 

1 

2 

3 

4 

17 

y% 

140.3 

91.5 

7 

0 

4000 

186 

17 

0 

10 

2 

6 

17 

Y 

151.5 

66.2 

7 

0 

6000 

280 

20 

1 

1 

3 

1 

18 

y? 

160.4 

92.3 

7 

0 

8000 

375 

23 

1 

3 

3 

7 

19 

1A 

169.3 

113.6 

7 

6 

4000 

212 

18 

0 

11 

2 

9 

18 

1A 

172.3 

84.3 

7 

6 

6000 

322 

22 

1 

1 

3 

3 

20 

1A 

191.4 

105.2 

7 

6 

8000 

429 

24 

1 

4 

3 

9 

20 

<A 

191.4 

137.4 

8 

0 

4000 

240 

19 

1 

0 

2 

10 

18 

IA 

184.1 

103.6 

8 

0 

6000 

363 

22 

3 

3 

6 

20 

204.6 

138.7 

8 

0 

8000 

487 

25 

1 

5 

4 

0 

21 

1A 

214.8 

166.3 

8 

6 

4000 

272 

20 

1 

0 

2 

11 

21 

1A 

228.7 

116.0 

8 

6 

6000 

410 

•24 

1 

3 

3 

8 

23 

1A 

250.5 

155.8 

8 

6 

8000 

546 

26 

1 

7 

4 

3 

21 

y* 

228.7 

209.7 

9 

0 

4000 

303 

21 

1 

1 

3 

2 

21 

Y 

242.6 

141.8 

9 

0 

6000 

456 

24 

1 

5 

3 

11 

22 

y* 

254.1 

198.5 

9 

0 

8000 

611 

27 

1 

8 

4 

6 

22 

y?, 

254.1 

247.4 

9 

6 

4000 

333 

21 

1 

3 

3 

5 

16 

% 

310.8 

183.4 

9 

6 

6000 

506 

25 

1 

6 

4 

1 

18 

5/s 

349.7 

233.2 

9 

6 

8000 

678 

29 

1 

9 

4 

9 

'19 

5/8 

369.1 

289.5 

10 

0 

4000 

370 

22 

1 

3 

3 

6 

17 

5/8 

348.1 

201.7 

10 

0 

6000 

559 

26 

1 

7 

4 

3 

19 

ys 

389.0 

271.6 

10 

0 

8000 

750 

30 

1 

10 

4 

11 

20 

N 

409.5 

333.5 

10 

6 

4000 

405 

23 

1 

4 

3 

8 

18 

5/8 

387.5 

237.0 

10 

6 

6000 

614 

28 

1 

8 

4 

7 

19 

ys 

409.0 

318.5 

10 

6 

8000 

822 

30 

2 

0 

5 

2 

20 

N 

430.5 

401.3 

11 

0 

4000 

442 

24 

1 

5 

3 

11 

18 

5/8 

406.4 

277.8 

11 

0 

6000 

671 

28 

1 

9 

4 

8 

20 

y* 

451.5 

363.0 

11 

0 

8000 

902 

33 

2 

0 

5 

5 

22 

ys 

496.7 

440.7 

11 

6 

4000 

484 

25 

1 

5 

4 

0 

20 

% 

472.5 

301.8 

11 

6 

6000 

731 

30 

1 

10 

4 

11 

21 

% 

496.1 

416.8 

11 

6 

8000 

983 

34 

2 

1 

5 

7 

22 

% 

519.8 

498.5 

12 

0 

4000 

524 

26 

1 

6 

4 

2 

22 

% 

542.9 

347.8 

12 

0 

6000 

792 

31 

1 

11 

5 

2 

22 

y& 

542.9 

475.9 

12 

0 

8000 

1067 

35 

2 

2 

5 

10 

24 

% 

592.2 

564.8 

12 

6 

4000 

566 

26 

1 

7 

4 

3 

23 

ys 

591.7 

396.0 

12 

6 

6000 

857 

32 

2 

0 

5 

4 

22 

% 

566.0 

537.0 

12 

6 

8000 

1158 

38 

2 

2 

6 

1 

26 

y» 

668.9 

611.4 

140 


USEFUL     DATA 


REINFORCED  CONCRETE  PILE  CAPS 

CARRYING  CAPACITY  OF  EACH  PILE  =  30  TONS 

fa=  16,000  Ib.  per  sq.  in.  Punching  shear  =  120  Ib.  per  sq.  in. 

/o=or  less  than  650  Ib.  per  sq.  in.  Bond  stress       =  100  Ib.  per  sq.  in. 


Pile 
Caps 


4  PILES 

Column  load    =232,000  Ib. 
Concrete  =  1 . 89  cu.  yd. 

Reinforcement  =11 5  Ib. 

t -.--£$* -.--^ , 

12"l«  T~<—  3-0-  -  -**— 3-0— ***_ 


Column  load    =  346,000  Ib. 
Concrete  =3.55  cu.  yd. 

Reinforcement  =  211  Ib. 


CBCCrt 


8  PILES 

Column  load     =  457,000  Ib. 
Concrete  =  5 . 56  cu.  yd. 

Reinforcement  =  365  Ib. 


tfOTf 

5  PILES 

Column  load    =287,000  Ib. 
Concrete  =3.17  cu.  yd. 

Reinforcement  =151  Ib. 


7  PILES 

Column  load     =  403,000  Ib. 
Concrete  =  4 . 24  cu.  yd. 

Reinforcement  =  208  Ib. 


LJ      U 

9  PILES 

Column  load    =  512,000  Ib. 
Concrete  =  6 . 89  cu.  yd. 

Reinforcement  =  37  5  Ib. 


141 


Pile 
Caps 


CORRUGATED      BAR      COMPANY,     INC. 


REINFORCED   CONCRETE  PILE  CAPS 

CARRYING  CAPACITY  OF  EACH  PILE  =  30  TONS 

/8=  16,000  Ib.  per  sq.  in.  Punching  shear  =  120  Ib.  per  sq.  in. 

/c=or  less  than  650  Ib.  per  sq.  in.         Bond  stress       =  100  Ib.  per  sq.  in. 


10  PILES 

Column  load    =  570,000  Ibs. 
Concrete  «=»  7 . 32  cu.  yds. 

Reinforcement  =  397  Ibs. 


Column  load    =  619,000  Ib. 
Concrete        .  =  10 . 04  cu.  yds. 
Reinforcement  =  51 5  Ibs. 


,  12; ii'-o"- -,— -* 

" 


Column  load    =  674,000  Ibs. 
Concrete  =  11 .39  cu.  yds. 

Reinforcement  =  614  Ibs. 


'^'        13  PILES 
Column  load    =  729,000  Ibs. 
Concrete  =  12 . 63  cu.  yds. 

Reinforcement  =  602  Ibs. 


:4 


142 


USEFUL      DATA 


Piles 


REINFORCED  CONCRETE  PILES 

.  _      Lenjrth  of  Pile  —  --  - 

k~S 

i     1    i     1     !  —  f—  [—  1  —  1    i     i     1     !     !    i     i     1     1     |     i 

U 

L  3-0"—  --*- 

i    !   i    !    i    !   !    i    i  -i    !    i   !    !   i    !    !    !    !    i 

variable  

Concrete  Mixture:  1:  2:  4 


Length 
of  Pile 

Diameter 
of  Pile 

Round  Bar 
Verticals 

HEAD  SPIRAL 

HOOPING 

TOE  SPIRAL 

Volume  of 
Concrete 
per  Pile 

Rounds 

Pitch 

Rounds 

Spacing 

Rounds 

Pitch 

ft. 

in. 

No. 

Size 

Size 

in. 

Size 

in. 

Size 

in. 

cu.  ft. 

14 

14 

6 

H 

H 

2 

K 

12 

M 

1M 

14.2 

16 

14 

6 

H 

H 

2 

M 

12 

M 

iii 

16.4 

18 

14 

6 

H 

K 

2 

M 

12 

H 

11A 

18.7 

20 

14 

6 

% 

H 

2 

M 

12 

M 

IIA 

20  9 

22 

16 

6 

5A 

A 

2 

k 

12 

H 

iy2 

29.9 

24 

16 

6 

% 

A 

2 

ik 

12 

H 

m 

32.8 

26 

16 

6 

% 

A 

2 

1A 

12 

1A 

VA 

35.8 

28 

16 

6 

% 

A 

2 

H 

12 

H 

1H 

38.7 

30 

16 

6 

% 

A 

2 

1A 

12 

H 

iH 

41.6 

32 

18 

8 

H 

H 

2 

y* 

12 

X 

1^ 

56.2 

34 

18 

8 

% 

H 

2 

H 

12 

H 

1^ 

59.9 

36 

18 

8 

% 

H 

2 

H 

12 

^ 

IH 

63.6 

38 

18 

8 

i 

^ 

2 

N 

12 

% 

IM 

67.4 

40 

18 

8 

i 

N 

2 

N 

12 

H 

iH 

71.1 

42 

20 

8 

\K 

^ 

1^ 

N 

12 

N 

1^         92.3 

44 

20 

8 

iy* 

H 

ifc 

N 

12 

N 

IHI 

96.9 

46 

20 

8 

IM 

y* 

IH 

M 

12 

N 

IK 

101.5 

48 

20 

8 

ik 

y* 

iM 

^ 

12 

M 

1^ 

106.1 

50 

20 

8 

IK 

H 

i« 

H 

12 

N 

iH 

110.7 

52 

22 

8 

1M 

^ 

i^ 

« 

12 

H 

!M 

138.8 

143 


CORRUGATED      BAR      COMPANY,     INC. 


EARTH  AND  WATER  PRESSURES 

p  =  intensity  of  pressure  at  any  depth  h. 
H  =  total  horizontal  pressure  above  A-B. 
M  =  moment  at  section  A-B. 


h 

EARTH  HORIZONTAL 
w>  =  1001b. 

EARTH  SURCHARGED 

M7=1001b. 

WATER 
w  =  62.51b. 

0.2948wfc 

H  = 

0.1474wfc2 

M  = 
0.5896w;fc3 

0.7034wfc 

H 

0.35llwhz 

M  = 
1.4068w;/i3 

Pwh 

#  = 
O.Sph 

M  = 
4Hh 

ft. 

Ib. 

Ib. 

in.  Ib. 

Ib. 

Ib. 

in.  Ib. 

Ib. 

Ib. 

in.  Ib. 

IT 

29 

15 

59 

70 

35 

141 

63 

31 

125 

2 

59 

59 

472 

141 

141 

1,125 

125 

125 

1,000 

3 

88 

132 

1,592 

211 

317 

3,798 

188 

281 

3,375 

4 

118 

236 

3,773 

281 

563 

9,003 

250 

500 

8,000 

5 

147 

368 

7,370 

352 

879 

17,584 

313 

781 

15,625 

6 

177 

531 

12,735 

422 

1,266 

30,385 

375 

1,125 

27,000 

7 

206 

721 

20,223 

492 

1,723 

48,251 

438 

1,531 

42,875 

8 

236 

944 

30,187 

563 

2,251 

72,025 

500 

2,000 

64,000 

9 

265 

1,193 

42,982 

633 

2,849 

102,551 

563 

2,531 

91,125 

10 

295 

1,475 

58,960 

703 

3,517 

140,673 

625 

3,125 

125,000 

11 

324 

1;782 

78,476 

774 

4,255 

187,236 

688 

3,781 

166,375 

12 

354 

2,124 

101,883 

844 

5,064 

243,084 

750 

4,500 

216,000 

13 

383 

2,490 

129,535 

914 

5,943 

309,060 

813 

5,281 

274,625 

14 

413 

2,891 

161,786 

985 

6,893 

386,008 

875 

6,125 

343,000 

15 

442 

3,315 

198,990 

1,055 

7,913 

474,773 

938 

7,031 

421,875 

16 

472 

3,776 

241,500 

,125 

9,003 

576,199 

1,000 

8,000 

512,000 

17 

501 

4,259 

289,670 

,196 

10,164 

691,129 

1,063 

9,031 

614,125 

18 

531 

4,779 

343,855 

,266 

11,395 

820,408 

1,125 

10,125 

729,000 

19 

560 

5,320 

404,407 

,336 

12,696 

964,879 

1,188 

11,281 

857,375 

20 

590 

5,900 

471,680 

,407 

14,067 

1,125,388 

1,250 

12,500 

1,000,000 

21 

619 

6,500 

546,029 

,477 

15,509 

1,302,777 

1,313 

13,781 

1,157,625 

22 

649 

7,139 

627,806 

,547 

17,021 

1,497,891 

1,375 

15,125 

1,331,000 

23 

678 

7,797 

717,366 

,618 

18,604 

1,711,574 

,438 

16,531 

1,520,875 

24 

708 

8,496 

815,063 

,688 

20,257 

1,944,670 

,500 

18,000 

1,728,000 

25 

737 

9,213 

921,250 

,758 

21,980 

2,198,023 

,563 

19,531 

1,953,125 

26 

766 

9,958 

1,036,280 

,829 

23,774 

2,472,479 

,625 

21,125 

2,197,000 

27 

796 

10,746 

1,160,509 

,899 

25,638 

2,768,876 

,688 

22,781 

2,460,375 

28 

825 

11,550 

1,294,290 

,969 

27,572 

3,088,064 

1,750 

24,500 

2,744,000 

29 

855 

12,398 

1,437,975 

2,040 

29,577 

3,430,885 

1,813 

26,281 

3,048,625 

30 

884 

13,260 

1,591,920 

2,110 

31,652 

3,798,184 

1,875 

28,1,25 

3,375,000 

31 

914 

14,167 

1,756,477 

2,180 

33,797 

4,190,803 

1,938 

30,031 

3,723,875 

32 

943 

15,088 

1,932,001 

2,251 

36,012 

4,609,588 

2,000 

32,000 

4,096,000 

33 

973 

16,045 

2,118,846 

2,321 

38,298 

5,055,382 

2,063 

34,031 

4,492,125 

34 

1,002 

17,034 

2,317,364 

2,391 

40,655 

5,529,030 

2,125 

36,125 

4,913,000 

35 

1,032 

18,060 

2,527,910 

2,462 

43,081 

6,031,375 

2,188 

38,281  5,359,375 

Angle  of  repose  =  33° 


144 


USEFUL      DATA 

Retaining 
'Walls 

-jit 

T 

*S^"%^s« 

4  —  \  —  1  —  I-  —  1-  —  h- 

CANTILEVER   RETAINING  WALLS 

J, 

4—  4-  +  -f-4--t 
4—  H--I  —  t—  4—4- 

SURFACE  OF  EARTH  HORIZONTAL 

'-. 

L 

4--f-4--f—  f-H- 

1? 

4  —  \  1  —  I  —  1  I- 
4--4—  t—  4--4--4- 

Angle  of  repose,  33°. 

,   I     . 

•JS&N 

4  —  1-  —  HT+TtT-f 
^H^fefT+T+T^ 

Weight  of  earth  100  Ib.  per  cu.  ft. 

r*-0-* 

L>  ?  \ 

tl^S|I±±± 

fs  =  16,000  Ib.  per  sq.  in. 

f              £*E(\  11^    ,            _    ;_^ 

?  E^  ^^l 

[  II     1  1  1  1  1 

jc—      ooU  ID.  per  sq.  in. 

L^ty~ 

i  i  i  ;  i  i  i  i  i 

n  =  15 

Section 


Elevation 


CONCRETE 


Height  of 
WallH 

a 

b 

c. 

Soil  Pressure 
at  Toe 

Soil  Pressure 
at  Heel 

Concrete  per  ft. 
Length  of  Wall 

ft. 

ft. 

in. 

ft. 

in. 

ft. 

in. 

Ib.  per  sq.  ft. 

Ib.  per  sq.  ft. 

cu.  ft. 

7 

1 

0 

1 

0 

1 

10 

1460 

90 

10.41 

8 

1 

1 

1 

1 

2 

1 

1470 

270 

12.35 

9 

1 

1 

1 

2 

2 

9 

1770 

130 

14.04 

10 

1 

2 

1 

4 

2 

10 

2000 

60 

16.14 

11 

1 

2 

1 

6 

3 

2 

2100 

90 

17.65 

12 

1 

3 

1 

8 

3 

7 

2210 

160 

20.37 

13 

1 

4 

1 

8 

4 

0 

2480 

120 

23.10 

14 

1 

4 

2 

1 

4 

3 

2400 

240 

24.95 

15 

1 

5 

2 

1 

4 

7 

2680 

200 

27.79 

16 

1 

5 

2 

2 

4 

11 

2870 

170 

29.45 

17 

1 

6 

2 

3 

5 

3 

3060 

160 

32.65 

18 

1 

7 

2 

4 

5 

7 

3280 

140 

36.00 

19 

1 

7 

2 

6 

6 

1 

3350 

230 

38.25 

20 

1 

8 

2 

8 

6 

6 

3430                 310 

42.13 

REINFORCEMENT 
Bars  in  all  Cases  of  Round  Section 


M  BAH8 


10'  6" 

11'  9" 

12'  9" 

14'  3" 

15'  3" 

16'  3" 

17'  6" 

18'  6" 

19'  6" 

20'  6" 

21'  6" 

22'  6" 


JV  BARS 


O  BARS 


y* 


3'  9" 

4'  3" 

4'  9" 

5'  0" 

5'  3" 

6'  3" 

6'  6" 

6'  6" 

7'  3" 

7'  3" 

8'  0" 

8'  3" 

8'  9" 

9'  0" 


y* 


OQ.S 

12 
12 
12 
10 

11 

11 
10 


2'  3" 

2'  3" 

2'  6" 

2'  9" 

3'  3" 

3'  3" 

4'  0" 

4'  0" 

4'  3" 

4'  3" 

4'  3" 

5'  0" 

5'  0" 


P  BARS 


y* 


u 


3'  0" 

3'  3" 

4'  3" 

4'  6" 

4'  9" 

5'  6" 

6'  6" 

6'  9" 

T  6" 

T  9" 

8'  0" 

8'  6" 

9'  3" 

9'  9" 


L  BARS 


6A 


14.4 

15.7 

21.3 

26.2 

32.3 

41.8 

63.4 

75.4 

88.9 

105.2 

122.2 

139.8 

174.7 

192.9 


Hooks  are  required  at  lower  end  of  M  and  AT  bars  for  walls  over  11'  0*  In  height. 


145 


Retaining 
Walls 


CORRUGATED      BAR      COMPANY,     INC. 


CANTILEVER  RETAINING  WALLS 

SURFACE  OF  EARTH  SURCHARGED 
Angle  of  repose,  33°. 

Weight  of  earth  100  Ib.  per  cu.  ft. 
/8=  16,000  Ib.  persq.  in. 
/c=      650  Ib.  per  sq.  in. 
n=15   x 


CONCRETE 


Height  of 
Walltf 

a 

6 

c 

Soil  Pressure 
at  Toe 

Soil  Pressure 
at  Heel 

Concrete  per  ft. 
Length  of  Wall 

ft. 

ft. 

in. 

ft. 

in. 

ft. 

in. 

Ib.  per  sq.  ft. 

Ib.  per  sq.  ft. 

cu.  ft. 

7 

1 

0 

1 

4 

2 

8 

2230 

270 

11.55 

8 

1 

11A 

1 

6 

3 

7^ 

2370 

510 

14.79 

9 

1 

3 

1 

8 

4 

1 

2700 

540 

18.12 

10 

1 

4^ 

1 

10 

4 

6^ 

3020 

580 

21.61 

11 

1 

6 

2 

0 

4 

8 

3300 

640 

24.90 

12 

1 

71A 

2 

3 

5 

1^ 

3730                 550 

29.12 

13 

1 

9 

2 

5 

5 

7 

4060                 580 

33.50 

14 

1 

10^ 

2 

8 

5 

9^ 

4340 

620 

37.90 

15 

2 

0 

2 

10 

6 

2 

4770 

550 

42.75 

16 

2 

1H 

3 

0 

6 

5^ 

5170 

510 

47.70 

17 

2 

3 

3 

2 

6 

11 

5490 

550 

53.28 

18 

2 

4^ 

3 

4 

7 

2K 

5930 

470 

58.85 

19 

2 

6 

3 

8 

7 

6 

6090 

550 

65.05 

20 

2 

7H 

4 

0 

7 

8H 

6330 

630                71.30 

REINFORCEMENT 
Bars  in  all  Cases  of  Round  Section 


M   BARS 


H 


18 


8'  6" 

9'  9" 

10'  9" 

12'  6" 


14 

17 

13 

16 

19^  13'  6" 
9" 
9" 
0" 

18' 0"! 
3"! 


18     20'  3"  iy8 


BARS 


IS 

i_s 

14 
17 
13 
16 


18 


4'  0" 
4'  6" 
5' 

6'  0" 
7'  6 
7'  9 
8'  6 
9'  0" 
9'  6 


0"! 
18     llO'  6"  iys 


16KH' 

18     |22'  6"1M  18     |ll' 
16^23'  9*1] 


BARS 


H 


0"iys 


18 
16J 
18 

*|18 


ft-lH 


5'  6" 
5'  9" 
6'  3" 
6'  6" 
6' 9" 
7'0» 
7'  6" 
V  9" 
8' 3" 
8'  6" 


O  BARS 


P  BARS 


8J^10' 

8 

7^10' 


0" 


6" 


L  BARS 


H 


fl 


18.9 

24.5 

33.8 

43.3 

49.5 

61.9 

85.0 

100.3 

122.4 

139.2 

164.0 

185.8 

215.7 

241.0 


Hooks  are  required  at  lower  end  of  M,  N  and  Q  bars  for  walls  over  9'  0"  in  height. 


146 


USEFUL      DATA 


Founda- 
tion 


FOUNDATIONS 

BEARING  CAPACITY  OF  SOILS 


Soil 

SAFE  BEARING  POWER  IN  TONS 
PER  SQUARE  FOOT 

Minimum 

Maximum 

Rock,  the  hardest,  in  thick  layers  in  native  bed  .    .    . 
Rock  equal  to  best  ashlar  masonry                .        ... 

200 
25 
15 
5 
6 
4 
1 
8 
4 
2 
0.5 

30 
20 
10 
8 
6 
2 
10 
6 
4 
1 

Rock  equal  to  best  brick  masonry  

Rock  equal  to  poor  brick  masonry      

Clay  in  thick  beds  always  dry 

Clay  in  thick  beds,  moderately  dry                .... 

Clay,  soft    

Gravel  and  coarse  sand,  well  cemented      

Sand  dry  compact  and  well  cemented 

Sand,  clean  dry 

Quicksand,  alluvial  soils,  etc.                                .... 

COEFFICIENTS  AND  ANGLES  OF  FRICTION 


Materials  in  Contact 

Coefficient 

Angle  of 
Friction 

Masonry  upon  masonry    

0.65 

33°  00' 

IVIasonry  upon  wood  with  grain 

0  60 

31°  00' 

Masonry  upon  wood,  across  grain 

0  50 

26°  40' 

Masonry  on  dry  clay                        .... 

0  50 

26°  40' 

Masonry  on  wet  clay     

0  33 

18°  20' 

Masonry  on  sand   

0  40 

21°  50' 

Masonry  on  gravel     

0.60 

31°  00' 

From  "A  Treatise  on  Masonry  Construction,"  by  Prof.  Ira  O.  Baker. 


147 


CORRUGATED      BAR      COMPANY,     INC. 


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OO        rH     rH        (M     <M        CO     "*        "*     to        CO     00        OOO        O     CO        <M     CO 

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148 


USEFUL      DATA 


VERTICAL  STEEL  REQUIRED  FOR  GIVEN  PERCENTAGES 
OF  ROUND  COLUMN  CORE  AREAS 


Column 
Verticals 
Percentages 
and  Areas 


Core 
Dia. 

in. 

Core 
Area 

PERCENT  OP  CORE  AREA 

0.5 

0.7E 

1.0 

1.5 

2.0 

2.5 

3.0 

3.5 

4.0 

5.0 

6.0 

7.0 

8.0 

sq.  in. 

Area  of  Vertical  Steel  in  Square  Inches 

12 
13 

113 
133 

0.57 
0.66 

0  85 

1.13 

1.70 

2.26 

2.83 

3  39 

3.96 

4  52 

5  65 

6  79 

7  92 

9  05 

1.00 

1.33 

1.99 

2.65 

3.32 

3.98 

4.65 

5.31 

6.64 

7.96 

9.29 

10.62 

14 

154 

0.77 

1.15 

1.54 

2.31 

3.08 

3.85 

4.62 

5.39 

6.16 

7.70 

9.24 

10.78 

12.32 

15 

177 

0.88 

1.33 

1.77 

2.65 

3.53 

4.42 

5.30 

6.19 

7.07 

8.84 

10.60 

12.37 

14.14 

16 

201 

1.01 

1.51 

2.01 

3.02 

4.02 

5.03 

6.03 

7.04 

8.04 

10.05 

12.06 

14.07 

16.08 

17 

227 

1.13 

1.70 

2.27 

3.40 

4.54 

5.67 

6.81 

7.94 

9.08 

11.35 

13.62 

15.89 

18.16 

18 

254 

1.27 

1.91 

2.54 

3.82 

5.09 

6.36 

7.63 

8.91 

10.18 

12.72 

15.27 

17.81 

20.36 

19 

284 

1.42 

2.13 

2.84 

4.25 

5.67 

7.09 

8.51 

9.92 

11.34 

14.18 

17.01 

19.85 

22.68 

20 

314 

1.57 

2.36 

3.14 

4.71 

6.28 

7.85 

9.42 

11.00 

12.57 

15.71 

18.85 

21.99 

25.13 

21 

346 

1.73 

2.60 

3.46 

5.20 

6.93 

8.66 

10.39 

12.12 

13.85 

17.32 

20.78 

24.25 

27.71 

22 

380 

1.90 

2.85 

3.80 

5.70 

7.60 

9.50 

11.40 

13.30 

15.21 

19.01 

22.81 

26.61 

30.41 

23 

415 

2.08 

3.12 

4.15 

6.23 

8.31 

10.39 

12.46 

14.54 

16.62 

20.77 

24.93 

29.08 

33.24 

24 

452 

2.26 

3.39 

4.52 

6.79 

9.05 

11.31 

13.57 

15.83 

18.10 

22.62 

27.14 

31.67 

36.19 

25 

491 

2.45 

3.68 

4.91 

7.36 

9.82 

12.27 

14.73 

17.18 

19.63 

24.54 

29.45 

34.36 

39.27 

26 

531 

2.65 

3.98 

5.31 

7.96 

10.62 

13.27 

15.93 

18.58 

21.24 

26.55 

31.86 

37.17 

42.47 

27 

573 

2.86 

4.29 

5.73 

8.59 

11.45 

14.31 

17.18 

20.04 

22.90 

28.63 

34.35 

40.08 

45.80 

28 

616 

3.08 

4.62 

6.16 

9.24 

12.32 

15.39 

18.47 

21.55 

24.63 

30.79 

36.95 

43.10 

49.26 

29 

661 

3.30 

4.95 

6.61 

9.91 

13.21 

16.51 

19.82 

23.12 

26.42 

33.03 

39.63 

46.24 

52.84 

30 

707 

3.53 

5.30 

7.07 

10.60 

14.14 

17.67 

21.21 

24.74 

28.27 

35.34 

42.41 

49.48 

56.55 

31 

755 

3.77 

5.66 

7.55 

11.32 

15.10 

18.87 

22.64 

26.42 

30.19 

37.74 

45.29 

52.83 

60.38 

32 

804 

4.02 

6.03 

8.04 

12.06 

16.08 

20.11 

24.13 

28.15 

32.17 

40.21 

48.25 

56.30 

64.34 

33 

855 

4.28 

6.41 

8.55 

12.83 

17.11 

21.38 

25.66 

29.94 

34.21 

42.76 

51.32 

59.87 

68.42 

34 

908 

4.54 

6.81 

9.08 

13.62 

18.16 

22.70 

27.24 

31.78 

36.32 

45.40 

54.48 

63.55 

72.63 

35 

962 

4.81 

7.22 

9.62 

14.43 

19.24 

24.05 

28.86 

33.67 

38.48 

48.11 

57.73 

67.35 

76.97 

36 

1018 

5.09 

7.63 

10.18 

15.27 

20.36 

25.45 

30.54 

35.63 

40.72 

50.89 

61.07 

71.25 

81.43 

149 


Column 

Spirals 

Pitch 

and 

Percentage 


II 


M          U 

o  g 


CORRUGATED   BAR   COMPANY,  INC. 


SbToo 


3JOO 


%       t-\«0\«j\.J\«*\«$\-H\Jxfc       t 

COCOCOCOCOCOCOCOCOINCO 


COCOCOCOCOCOCOCOCslCOCOT-liHTHTHr-li-lCOTHi-l 


CO  CO  CO  CO  CO  M  CO  CO  CO    CO  CO  CO  CO 


%     «o\  »o\  »-*\  P*S  i-N  ^     ^ 

eocococococococo 


coeococoeocococococococo 


*    %    %    ft 


150 


USEFUL      DATA 


COLUMN  SPIRALS 

WEIGHT  IN  POUNDS  PER  FOOT  OF  HEIGHT 

(Weights  do  not  Include  Spacers) 

.NO.  O  WIRE — EQUIVALENT—  ROUND  BAR 

4 

Based  on  American  Steel  and  Wire  Co.'s  Standard  Gauge 


Diameter 
of 
Spiral 

PITCH  OF  SPIRAL  IN  INCHES 

*Factor  to 
Add  for 
Finishing 
Spiral 

in. 

1H 

HI 

2 

2M 

2M 

2M 

3 

3^ 

4 

b. 

12 

4.10 

3.51 

3.08 

2.74 

2.47 

2.24 

2.06 

1.77 

1.55 

1.30 

13 

4.43 

3.80 

3.32 

2.96 

2.66 

2.42 

2.22 

1.91 

1.68 

1.40 

14 

4.76 

4.08 

3.57 

3.18 

2.86 

2.60 

2.39 

2.05 

1.80 

1.50 

15 

5.09 

4.36 

3.82 

3.39 

3.06 

2.78 

2.55 

2.19 

1.92 

1.55 

16 

5.42 

4.65 

4.07 

3.61 

3.26 

2.96 

2.72 

2.33 

2.05 

1.60 

17 

5.75 

4.93 

4.31 

3.83 

3.46 

3.14 

2.88 

2.47 

2.17 

1.70 

18 

6.08 

5.21 

4.56 

4.05 

3.65 

3.32 

3.05 

2.61 

2.29 

1.80 

19 

6.41 

5.49 

4.81 

4.27 

3.85 

3.50 

3.21 

2.75 

2.41 

1.90 

20 

6.74 

5.78 

5.06 

4.49 

4.05 

3.68 

3.38 

2.90 

2.54 

2.00 

21 

7.07 

6.06 

5.31 

4.71 

4.25 

3.86 

3.54 

3.04 

2.66 

2.05 

22 

7.40 

6.34 

5.55 

4.92 

4.45 

4.04 

3.71 

3.18 

2.78 

2.10 

23 

7.73 

6.63 

5.80 

5.16 

4.64 

4.22 

3.87 

3.32 

2.91 

2.20 

24 

8.06 

6.91 

6.05 

5.38 

4.84 

4.40 

4.04 

3.46 

3.03 

2.30 

25 

8.39 

7.19 

6.30 

5.60 

5.04 

4.58 

4.20 

3.60 

3.15 

2.40 

26 

8.72 

7.47 

6.54 

5.82 

5.24 

4.76 

4.37 

3.74 

3.28 

2.50 

27 

9.05 

7.76 

6.79 

6.04 

5.43 

4.94 

4.53 

3.88 

3.40 

2.55 

28 

9.38 

8.04 

7.04 

6.26 

5.63 

5.12 

4.70 

4.02 

3.52 

2.60 

29 

9.71 

8.33 

7.29 

6.48 

5.83 

5.30 

4.86 

4.17 

3.65 

2.70 

30 

10.04 

8.61 

7.53 

6.70 

6.03 

5.48 

5.03 

4.31 

3.77 

2.80 

31 

10.37 

8.89 

7.78 

6.92 

6.23 

5.66 

5.19 

4.45 

3.89 

2.90 

32 

10.70 

9.17 

8.03 

7.14 

6.42 

5.84 

5.36 

4.59 

4.02 

3.00 

33 

11.03 

9.46 

8.28 

7.36 

6.62 

6.02 

5.52 

4.73 

4.14 

3.05 

34 

11.36 

9.74 

8.52 

7.58 

6.82 

6.20 

5.68 

4.87 

4.26 

3.10 

35 

11.69 

10.02 

8.77 

7.80 

7.02 

6.38 

5.85 

5.01 

4.39 

3.20 

36 

12.02 

10.31 

9.02 

8.02 

7.22 

6.56 

6.01 

5.15 

4.51 

3.30 

37 

12.35 

10.59 

9.27 

8.24 

7.42 

6.74 

6.18 

5.30 

4.64 

3.40 

38 

12.68 

10.87 

9.52 

8.46 

7.61 

6.92 

6.35 

5.44 

4.76 

3.50 

*  Weight  of  one  extra  turn  at  top  and  bottom  of  spiral. 

151 


CORRUGATED      BAR      COMPANY,     INC. 


COLUMN  SPIRALS 

WEIGHT  IN  POUNDS  PER  FOOT  OF  HEIGHT 
(Weights  do  not  Include  Spacers) 

NO.   0  WIRE — EQUIVALENT  —  ROUND  BAR 

16 

Based  on  American  Steel  and  Wire  Co.'s  Standard  Gauge 


Diameter 
of 
Spiral 

PITCH  OF  SPIRAL  IN  INCHES 

*Factor  to 
Add  for 
Finishing 
Spiral 

in. 

1J* 

1% 

2 

2M 

2^ 

2M 

3 

3^ 

4 

Ib. 

12 

6.48 

5.56 

4.87 

4.33 

3.90 

3.55 

3.26 

2.80 

2.46 

2.05 

13 

7.00 

6.01 

5.26 

4.68 

4.22 

3.83 

3.52 

3.02 

2.65 

2.20 

14 

7.53 

6.46 

5.65 

5.03 

4.53 

4.12 

3.78 

3.25 

2.85 

2.40 

15 

8.05 

6.90 

6.04 

5.36 

4.84 

4.40 

4.04 

3.47 

3.04 

2^45 

16 

8.57 

7.35 

6.44 

5.72 

5.15 

4.69 

4.30 

3.69 

3.24 

2.50 

17 

9.10 

7.80 

6.83 

6.07 

5.47 

4.97 

4.56 

3.92 

3.43 

2.70 

18 

9.62 

8.25 

7.22 

6.44 

5.78 

5.26 

4.82 

4.14 

3.63 

2.85 

19 

10.14 

8.70 

7.61 

6.77 

6.09 

5.54 

5.08 

4.36 

3.82 

3.00 

20 

10.66 

9.14 

8.00 

7.10 

6.41 

5.83 

5.34 

4.59 

4.02 

3.15 

21 

11.19 

9.59 

8.39 

7.46 

6.72 

6.11 

5.60 

4.81 

4.21 

3.25 

22 

11.71 

10.04 

8.78 

7.78 

7.03 

6.40 

5.86 

5.03 

4.41 

3.30 

23 

12.23 

10.49 

9.18 

8.16 

7.35 

6.68 

6.13 

5.26 

4.60 

3.50 

24 

12.75 

10.93 

9.57 

8.51 

7.66 

6.97 

6.39 

5.48 

4.80 

3.65 

25 

13.28 

11.38 

9.96 

8.88 

7.97 

7.25 

6.65 

5.70 

4.99 

3.80 

26 

13.80 

11.83 

10.35 

9.20 

8.29 

7.53 

6.91 

5.93 

5.19 

3.95 

27 

14.32 

12.28 

10.74 

9.55 

8.60 

7.82 

7.17 

6.15 

5.39 

4.05 

28 

14.84 

12.73 

11.13 

9.90 

8.91 

8.10 

7.43 

6.37 

5.58 

4.10 

29 

15.37 

13.17 

11.53 

10.25 

9.22 

8.39 

7.69 

6.60 

5.78 

4.30 

30 

15.89 

13.62 

11.92 

10.60 

9.54 

8.67 

7.95 

6.82 

5.97 

4.40 

31 

16.41 

14.07 

12.31 

10.95 

9.85 

8.96 

8.21 

7.04 

6.15 

4.60 

32 

16.94 

14.52 

12.70 

11.29 

10.16 

9.24 

8.47 

7.27 

6.36 

4.75 

33 

17.46 

14.97 

13.09 

11.64 

10.48 

9.53 

8.73 

7.49 

6.56 

4.80 

34 

17.98 

15.41 

13.48 

11.99 

10.79 

9.81 

8.99 

7.71 

6.75 

4.90 

35 

18.50 

15.86 

13.88 

12.34 

11.10 

10.10 

9.26 

7.94 

6.95 

5.05 

36 

19.02 

16.31 

14.27 

12.69 

11.42 

10.38 

9.52 

8.16 

7.14 

5.20 

37 

19.54 

16.75 

14.67 

13.04 

11.74 

10.66 

9.78 

8.38 

7.34 

5.40 

38 

20.06 

17.20 

15.06 

13.38 

12.04 

10.95 

10.04 

8.61 

7.53 

5.55 

*  Weight  of  one  extra  turn  at  top  and  bottom  of  spiral. 

152 


USEFUL      DATA 


COLUMN  SPIRALS 

WEIGHT  IN  POUNDS  PER  FOOT  OF  HEIGHT 
(Weights  do  not  Include  Spacers) 

XT         3  3" 

.N  0.  TT  WIRE — EQUIVALENT  —  ROUND  BAR 
U  o 

Based  on  American  Steel  and  Wire  Co.'s  Standard  Gauge 


Column 

Spiral 

Weights 


Diameter 
of 
Spiral 

PITCH  OP  SPIRAL  IN  INCHES 

*Factor  to 
Add  for 
Finishing 
Spiral 

in. 

1H         W 

2 

2M 

21A 

tK 

3 

3^ 

4 

To. 

12 

9.02 

7.73 

6.77 

6.02 

5.43 

4.94 

4.53 

3.89 

3.42 

2.85 

13 

9.74 

8.36 

7.32 

6.51 

5.85 

5.33 

4.89 

4.21 

3.69 

3.05 

14 

10.47 

8.98 

7.86 

6.97 

6.30 

5.73 

5.26 

4.52 

3.96 

3.30 

15 

11.20 

9.60 

8.41 

7.46 

6.73 

6.13 

5.62 

4.83 

4.23 

3.40 

16 

11.92 

10.22 

8.95 

7.94 

7.17 

6.52 

5.98 

5.14 

4.50 

3.50 

17 

12.65 

10.85 

9.49 

8.43 

7.60 

6.92 

6.35 

5.45 

4.77 

3.75 

18 

13.38 

11.47 

10.04 

8.91 

8.04 

7.31 

6.71 

5.74 

5.05 

3.95 

19 

14.11 

12.09 

10.59 

9.40 

8.48 

7.71 

7.07 

6.05 

5.32 

4.20 

20 

14.83 

12.72 

11.13 

9.88 

8.91 

8.10 

7.43 

6.38 

5.59 

4.40 

21 

15.56 

13.34 

11.68 

10.37 

9.35 

8.50 

7.80 

6.69 

5.86 

4.50 

22 

16.29 

13.96 

12.22 

10.83 

9.78 

8.90 

8.16 

6.99 

6.13 

4.60 

23 

17.01 

14.59 

12.77 

11.36 

10.22 

9.29 

8.52 

7.31 

6.40 

4.85 

24 

17.74 

15.21 

13.31 

11.83 

10.65 

9.69 

8.88 

7.62 

6.67 

5.10 

25 

18.47 

15.83 

13.86 

12.32 

11.09 

10.09 

9.25 

7.93 

6.93 

5.30 

26 

19.19 

16.45 

14.40 

12.80 

11.53 

10.48 

9.61 

8.24 

7.22 

5.50 

27 

19.92 

17.08 

14.95 

13.29 

11.96 

10.88 

9.95 

8.55 

7.49 

5.60 

28 

20.65 

17.70 

15.49 

13.77 

12.40 

11.27 

10.34 

8.86 

7.76 

5.70 

29 

21.37 

18.32 

16.04 

14.26 

12.83 

11.67 

10.70 

9.17 

8.03 

6.00 

30 

22.10 

18.95 

16.58 

14.74 

13.27 

12.06 

11.08 

9.48 

8.30 

6.10 

31 

22.83 

19.57 

17.12 

15.22 

13.70 

12.46 

11.42 

9.79 

8.57 

6.40 

32 

23.55 

20.19 

17.67 

15.71 

14.14 

12.86 

11.79 

10.11 

8.85 

6.60 

33 

24.28 

20.82 

18.21 

16.19 

14.57 

13.25 

12.15 

10.42 

9.12 

6.70 

34 

25.01 

21.44 

18.76 

16.68 

15.01 

13.65 

12.51 

10.73 

9.37 

6.80 

35 

25.74 

22.06 

19.30 

17.17 

15.45 

14.04 

12.89 

11.04 

9.66 

7.00 

36 

26.45 

22.68 

19.85 

17.65 

15.88 

14.44 

13.24 

11.35 

9.93 

7.20 

37 

27.18 

23.31 

20.40 

18.13 

16.33 

14.83 

13.59 

11.66 

10.21 

7.50 

38 

27.91 

23.92 

20.95 

18.62 

16.75 

15.23 

13.99 

11.96 

10.47 

7.70 

*  Weight  of  one  extra  turn  at  top  and  bottom  of  spiral. 

153 


CORRUGATED   BAR   COMPANY,  INC. 


COLUMN  SPIRALS 

WEIGHT  IN  POUNDS  PER  FOOT  OF  HEIGHT 
(Weights  do  not  Include  Spacers) 

NO.  -^  WIRE— EQUIVALENT  _  ROUND  BAR 
0  lo 

Based  on  American  Steel  and  Wire  Co.'s  Standard  Gauge 


Diameter 
of 
Spiral 

PITCH  OF  SPIRAL  IN  INCHES 

*Factor  to 
Add  for 
Finishing 
Spiral 

in. 

\H 

1M 

2 

2M 

234 

2M 

3 

3H 

4 

Ib. 

12 

12.72 

10.91 

9.56 

8.50 

7.66 

6.97 

6.40 

5.49 

4.82 

4.00 

13 

13.75 

11.79 

10.33 

9.18 

8.27 

7.53 

6.91 

5.93 

5.21 

4.30 

14 

14.78 

12.67 

11.09 

9.87 

8.89 

8.09 

7.42 

6.37 

5.59 

4.70 

15 

15.80 

13.55 

11.86 

10.55 

9.50 

8.65 

7.93 

6.81 

5.97 

4.80 

16 

16.83 

14.43 

12.63 

11.23 

10.12 

9.20 

8.44 

7.24 

6.36 

4.90 

17 

17.85 

15.31 

13.40 

11.92 

10.73 

9.76 

8.95 

7.67 

6.74 

5.30 

18 

18.88 

16.19 

14.17 

12.60 

11.35 

10.32 

9.46 

8.11 

7.12 

5.60 

19 

19.91 

17.07 

14.94 

13.28 

11.96 

10.88 

9.98 

8.54 

7.50 

5.90 

20 

20.93 

17.95 

15.71 

13.97 

12.58 

11.44 

10.49 

9.00 

7.89 

6.20 

21 

21.96 

18.82 

16.48 

14.65 

13.19 

12.00 

11.00 

9.44 

8.27 

6.40 

22 

22.98 

19.70 

17.25 

15.33 

13.81 

12.56 

11.51 

9.88 

8.63 

6.50 

23 

24.01 

20.58 

18.01 

16.02 

14.42 

13.11 

12.02 

10.32 

9.04 

6.90 

24 

25.03 

21.46 

18.78 

16.70 

15.04 

13.67 

12.54 

10.75 

9.42 

7.20 

25 

26.06 

22.34 

19.55 

17.38 

15.65 

14.23 

13.05 

11.18 

9.78 

7.50 

26 

27.09 

23.22 

20.32 

18.07 

16.26 

14.79 

13.56 

11.62 

10.19 

7.75 

27 

28.11 

24.10 

21.09 

18.75 

16.88 

15.35 

14.07 

12.05 

10.57 

7.95 

28 

29.14 

24.98 

21.86 

19.43 

17.49 

15.91 

14.60 

12.49 

10.93 

8.05 

29 

30.16 

25.86 

22.63 

20.12 

18.11 

16.47 

15.09 

12.95 

11.34 

8.45 

30 

31.19 

26.74 

23.40 

20.80 

18.72 

17.02 

15.61 

13.39 

11.70 

8.65 

31 

32.21 

27.61 

24.17 

21.48 

19.34 

17.58 

16.12 

13.82 

12.08 

9.05 

32 

33.24 

28.49 

24.93 

22.17 

19.95 

18.13 

16.65 

14.26 

12.48 

9.30 

33 

34.22 

29.37 

25.70 

22.85 

20.57 

18.70 

17.14 

14.70 

12.87 

9.40 

34 

35.26 

30.25 

26.47 

23.53 

21.18 

19.26 

17.65 

15.14 

13.23 

9.60 

35 

36.30 

31.13 

27.24 

24.22 

21.80 

19.82 

18.17 

15.56 

13.63 

9.90 

36 

37.30 

32.01 

28.01 

24.90 

22.41 

20.38 

18.68 

16.00 

14.00 

10.20 

37 

38.32 

32.90 

28.80 

25.60 

23.05 

20.93 

19.20 

16.46 

14.41 

10.60 

38 

39.35 

33.77 

29.58 

26.29 

23.62 

21.49 

19.72 

16.90 

14.78 

10.90 

Weight  of  one  extra  turn  at  top  and  bottom  of  spiral. 

154 


USEFUL      DATA 


COLUMN  SPIRALS 

WEIGHT  IN  POUNDS  PER  FOOT  OF  HEIGHT 

(Weights  do  not  Include  Spacers) 

"NT         7  1 " 

JN  O.  —  WIRE — EQUIVALENT  —  ROUND  BAR 

Based  on  American  Steel  and  Wire  Co.'s  Standard  Gauge 


Diameter 
of 
Spiral 

PITCH  OF  SPIRAL  IN  INCHES 

*Factor  to 
Add  for 
Finishing 
Spiral 

in. 

iy2 

1M 

2 

2k' 

2^ 

2M 

3 

3H 

4 

Ib. 

12 

16.52 

14.15 

12.41 

11.04 

9.96 

9.03 

8.30 

7.14 

6.26 

5.20 

13 

17.85 

15.31 

13.39 

11.92 

10.74 

9.77 

8.96 

7.70 

6.76 

5.60 

14 

19.18 

16.45 

14.40 

12.81 

11.54 

10.48 

9.63 

8.27 

7.26 

6.10 

15 

20.52 

17.59 

15.40 

13.67 

12.34 

11.22 

10.28 

8.84 

7.75 

6.25 

16 

21.85 

18.75 

16.40 

14.56 

13.14 

11.93 

10.96 

9.39 

8.27 

6.40 

17 

23.18 

1.9.88 

17.38 

15.44 

13.95 

12.67 

11.61 

9.96 

8.75 

6.90 

18 

24.52 

21.01 

18.40 

16.33 

14.73 

13.40 

12.29 

10.52 

9.23 

7.25 

19 

25.84 

22.14 

19.40 

17.22 

15.53 

14.11 

12.94 

11.09 

9.72 

7.65 

20 

27.17 

23.30 

20.40 

18.10 

16.33 

14.85 

13.62 

11.69 

10.24 

8.00 

21 

28.51 

24.44 

21.41 

18.99 

17.13 

15.56 

14.28 

12.26 

10.74 

8.30 

22 

29.84 

25.56 

22.38 

19.84 

17.94 

16.30 

14.95 

12.83 

11.21 

8.40 

23 

31.17 

26.73 

23.39 

20.79 

18.72 

17.03 

15.61 

13.39 

11.73 

8.90 

24 

32.50 

27.86 

24.39 

21.68 

19.52 

17.75 

16.28 

13.96 

12.23 

9.30 

25 

33.83 

29.00 

25.40 

22.57 

20.32 

18.48 

16.94 

14.53 

12.70 

9.70 

26 

35.16 

30.12 

26.37 

23.46 

21.12 

19.20 

17.61 

15.08 

13.22 

10.00 

27 

36.50 

31.29 

27.38 

24.34 

21.89 

19.93 

18.27 

15.64 

13.72 

10.30 

28 

37.83 

32.43 

28.38 

25.23 

22.71 

20.65 

18.94 

16.21 

14.19 

10.40 

29 

39.16 

33.59 

29.38 

26.12 

23.51 

21.38 

19.60 

16.81 

14.72 

11.00 

30 

40.49 

34.71 

30.36 

27.00 

24.31 

22.10 

20.28 

17.38 

15.21 

11.20 

31 

41.82 

35.85 

31.37 

27.89 

25.11 

22.83 

20.93 

17.95 

15.68 

11.70 

32 

43.14 

36.97 

32.38 

28.78 

25.90 

23.55 

21.61 

18.52 

16.21 

12.10 

33 

44.47 

38.14 

33.38 

29.67 

26.70 

24.28 

22.26 

19.08 

16.70 

12.20 

34 

45.80 

39.28 

34.35 

30.55 

27.50 

25.00 

22.90 

19.65 

17.18 

12.50 

35 

47.13 

40.40 

35.36 

31.44 

28.30 

25.73 

23.59 

20.20 

17.70 

12.90 

36 

48.46 

41.57 

36.37 

32.33 

29.10 

26.46 

24.23 

20.76 

18.18 

13.30 

37 

49.80 

42.70 

37.38 

33.22 

29.92 

27.18 

24.92 

21.37 

18.71 

13.80 

38 

51.13 

43.83 

38.38 

34.11 

30.68 

27.90 

25.60 

21.93 

19.19 

14.20 

*  Weight  of  one  extra  turn  at  top  and  bottom  of  spiral. 

155 


Column 
Spirals 
Wire  and 
Spacers 


CORRUGATED      BAR      COMPANY,     INC. 


COLUMN  SPIRALS 

STANDARD  WIRE  AND  SPACERS 
STANDARD  WIRE 


Gauge 

Practical 
Equiv. 

Diameter 

Area 

Wt.perlin.ft. 

No. 

Rod 

in. 

sq.  in. 

Ib. 

3 

w* 

0.2437 

0.0467 

0.1578 

0     . 

A"* 

0.3065 

0.0740 

0.2497 

$ 

H'* 

0.3625 

0.1029 

0.3473 

* 

&•> 

0.4305 

0.1453 

0.4901 

i 

Mft 

0.4900 

0.1886 

0.6363 

American  Steel  &  Wire  Co.  Gauges. 

STANDARD  SPACERS 


SPIRAL 

WIRE 

T-SECTION  SPACERS 

Diam. 
in. 

Height 
ft. 

Gauge 

Practical 
Equiv. 

Size 

Wt.  per  ft. 
for  two 
Spacers 

9  to  15 

ItolS 

3 

M*4> 

1       x  1       x  Y% 

1.60 

16  to  30 

1  to  20 

3 

X"* 

iMxlMx^ 

2.00 

9  to  15 

1  to  15 

0 

A"4> 

IMxl^xK 

2.00 

16  to  30 

1  to  20 

0 

&"<!> 

l^xlMx^ 

2.96 

9  to  15 

1  to  15 

4 

yt* 

lMxlMx^-3 

2.00 

16  to  30 

1  to  20 

I 

y** 

iMxiMx^ 

2.96 

9  to  30 

1  to  20 

« 

A> 

l^xl^x^ 

3.60 

9  to  30 

Ito20 

i 

1A"$ 

l^xl^x-A 

3.60 

NOTE. — For  spirals  over  30  inches  in  diameter  use  twice  the  num- 
ber of  spacers  specified  for  spirals  under  30  inches  in  diameter. 


156 


USEFUL      DATA 


COLUMNS 

AREAS,  PERIMETERS,  WEIGHTS,  VOLUMES  AND  MOMENTS  OF  INERTIA 
NOTE — Moments  of  Inertia  calculated  about  Axis  A-A 


Column 
"Sections 


,._..          ^^ 

A 

<     A-C—  ~—L 

d 

r         i 

>.       / 

Area 

Peri- 

Weight 

Volume 

Moment 

Area 

Peri- 

Weight 

Volume 

Moment 

meter 

per  ft. 

per  ft. 

of  Inertia 

meter 

per  ft. 

per  ft. 

of  Inertia 

in. 

sq.  in. 

in. 

Ib. 

cu.  ft. 

in.4 

sq.  in. 

in. 

Ib. 

cu.  ft. 

in.4 

12 

113.1 

37.70 

117.8 

0.78 

1018 

119.3 

39.76 

124.3 

0.83 

1136 

13 

132.7 

40.84 

138.2 

0.92 

1402 

140.0 

43.08 

145.8 

0.97 

1565 

14 

153.9 

43.98 

160.3 

.07 

1886 

162.4 

46.39 

169.2 

1.12 

2105 

15 

176.7 

47.12 

184.1 

.22 

2485 

186.4 

49.70 

194.2 

1.29 

2775 

16 

201.1 

50.27 

209.5 

.40 

3217 

212.1 

53.02 

220.9 

1.47 

3591 

17 

227.0 

53.41 

236.5 

.57 

4100 

239.4 

56.33 

249.4 

1.66 

4577 

18 

254.5 

56.55 

265.1 

.77 

5153 

268.4 

59.65 

279.6 

1.86 

5753 

19 

283.5 

59.69 

295.3 

.97 

6397 

299.1 

62.99 

311.6 

2.08 

7142 

20 

314.2 

62.83 

327.3 

2.18 

7854 

331.4 

66.27 

345.2 

2.30 

8768 

21 

346.4 

65.97 

360.8 

2.40 

9547 

365.3 

69.59 

380.5 

2.53 

10658 

22 

380.1 

69.12 

395.9 

2.64 

11499 

401.0 

72.90 

417.7 

2.78 

12837 

23 

415.5 

72.26 

432.8 

2.88 

13737 

438.2 

76.21 

456.5 

3.04 

15335 

24 

452.4 

75.40 

471.2 

3.14 

16286 

477.2 

79.53 

497.1 

3.31 

18181 

25 

490.9 

78.54 

511.4 

3.41 

19175 

517.8 

82.84 

539.4 

3.59 

21406 

26 

530.9 

81.68 

553.0 

3.69 

22432 

560.0 

86.16 

583.3 

3.89 

25042 

27 

572.6 

84.82 

596.5 

3.97 

26087 

603.9 

89.47 

629.1 

4.19 

29123 

28 

615.8 

87.96 

641.5 

4.27 

30172 

649.5 

92.78 

676.6 

4.51 

33683 

29 

660.5 

91.11 

688.0 

4.59 

34719 

696.7 

96.10 

725.7 

4.84 

38759 

30 

706.9 

94.25 

736.3 

4.91 

39761 

745.6 

99.41 

776.7 

5.17 

44388 

31 

754.8 

97.39 

786.2 

5.24 

45333 

796.1 

102.72 

829.3 

5.52 

50609 

32 

804.2 

100.53 

837.7 

5.58 

51472 

848.3 

106.04 

883.6 

5.89 

57462 

33 

855.3 

103.67 

890.9 

5.94 

58214 

902.2 

109.35 

939.8 

6.26 

64988 

34 

907.9 

106.81 

945.7 

6.30 

65597 

957.7 

112.66 

997.6 

6.64 

73231 

35 

962.1 

109.96 

1002.2 

6.68 

73662 

1014.8 

115.98 

1057.1 

7.04 

82234 

36 

1017.9 

113.10 

1060.3 

7.06 

82448 

1073.6 

119.29 

1118.3 

7.45 

92043 

37 

1075.2 

116.24 

1120.0 

7.47 

91998 

1134.1 

122.61 

1181.3 

7.87 

102704 

38 

1134.1 

119.38 

1181.3 

7.87 

102354 

1196.3 

125.92 

1246.1 

8.30 

114265 

39 

1194.6 

122.52 

1244.4 

8.29 

113561 

1260.0 

129.23 

1312.5 

8.74 

126777 

40 

1256.6 

125.66 

1308.9 

8.72 

125664 

1325.5 

132.55 

1380.7 

9.20 

140288 

157 


CORRUGATED   BAR   COMPANY,  INC. 


COLUMNS 

AREAS,  PERIMETERS,  WEIGHTS,  VOLUMES  AND  MOMENTS  OF  INERTIA. 
NOTE. — Moments  of  Inertia  calculated  about  Axis  A-A 


A,  
j 

*  IV 

<J         A 

A 

d 

Q>       A— 

&    A 

•i 

---    A 

Area 

Peri- 
meter 

Weight 
per  ft. 

Volume 
per  ft. 

Moment 
of  Inertia 

Area 

Weight 
per  ft. 

Volume 
per  ft. 

Moment 
of  Inertia 

in. 

sq.  in. 

in. 

Ib. 

cu.  ft. 

in.4 

sq.  in. 

Ib. 

cu.  ft. 

in.4 

12 

144 

48 

150.0 

1.00 

1728 

12.0 

12.5 

0.083 

144 

13 

169 

52 

176.0 

1.17 

2380 

13.0 

13.5 

0.090 

183 

14 

196 

56 

204.2 

1.36 

3201 

14.0 

14.6 

0.097 

229 

15 

225 

60 

234.4 

1.56 

4219 

15.0 

15.6 

0.104 

281 

16 

256 

64 

266.7 

1.78 

5461 

16.0 

16.7 

0.111 

341 

17 

289 

68 

301.0 

2.01 

6960 

17.0 

17.7 

0.118 

409 

18 

324 

72 

337.5 

2.25 

8748 

18.0 

18.8 

0.125 

486 

19 

361 

76 

376.0 

2.51 

10860 

19.0 

19.8 

0.132 

572 

20 

400 

80 

416.7 

2.78 

13333 

20.0 

20.8 

0.139 

667 

21 

441 

84 

459.4 

3.06 

16207 

21.0 

21.9 

0.146 

772 

22 

484 

88 

504.2 

3  36 

19521 

22.0 

22.9 

0.153 

887 

23 

529 

92 

551.0 

3.67 

23320 

23.0 

24.0 

0.160 

1014 

24 

576 

96 

600.0 

4.00 

27648 

24.0 

25.0 

0.167 

1152 

25 

625 

100 

651.0 

4.34 

32552 

25.0 

26.1 

0.173 

1302 

26 

676 

104 

704.2 

4.69 

38081 

26.0 

27.1 

0.181 

1465 

27 

729 

108 

759.4 

5.06 

44287 

27.0 

28.1 

0.187 

1640 

28 

784 

112 

816.7 

5.44 

51221 

28.0 

29.2 

0.194 

1829 

29 

841 

116 

876.0 

5.84 

58940 

29.0 

30.2 

0.201 

2032 

30 

900 

120 

937.5 

6.25 

67500 

30.0 

31.2 

0.208 

2250 

31 

961 

124 

1001.0 

6.67 

76960 

31.0 

32.3 

0.215 

2483 

32 

1024 

128 

1066.7 

7.12 

87381 

32.0 

33.3 

0.222 

2731 

33 

1089 

132 

1134.4 

7.56 

96827 

33.0 

34.4 

0.229 

2995 

34 

1156 

136 

1204.2 

8.03 

111361 

34.0 

35.4 

0.236 

3275 

35 

1225 

140 

1276.0 

8.50 

125052 

35.0 

36.5 

0.243 

3573 

36 

1296 

144 

1350.0 

9.00 

139968 

36.0 

37.5 

0.250 

3880 

37 

1369 

148 

1426.0 

9.50 

156180 

37.0 

38.5 

0.257 

4221 

38 

1444 

152 

1504.2 

10.02 

173761 

38.0 

39.6 

0.264 

4573 

39 

1521 

156 

1584.4 

10.57 

192787 

39.0 

40.6 

0.271 

4943 

40 

1600 

160 

1666.7 

11.11 

213333 

40.0 

41.7 

0.278 

5333 

158 


USEFUL      DATA 


Moments 
of  Inertia 


Dia. 
•<. of- > 

Circle 


MOMENT  OF  INERTIA 

OF  COLUMN  VERTICALS  ARRANGED  IN  A  CIRCLE 
EXPRESSED  IN  TERMS  OF  CONCRETE 

INCHES4 

7=n/8 


Diameter 
of 
Circle 

n=12 

n  =  15 

Percentage  of  Column  Verticals 

Percentage  of  Column  Verticals 

in. 

1% 

2% 

3% 

4% 

1% 

2% 

3% 

4% 

12 

244 

488 

732 

976 

305 

610 

915 

1220 

13 

336 

672 

1008 

1344 

420 

840 

1261 

1681 

14 

452 

904 

1356 

1808 

565 

1130 

1696 

2261 

15 

596 

1192 

1787 

2383 

745 

1491 

2234 

2979 

16 

771 

1543 

2314 

3085 

964 

1928 

2893 

3857 

17 

983 

1966 

2949 

3932 

1229 

2458 

3686 

4915 

18 

1235 

2471 

3706 

4942 

1544 

3089 

4633 

6178 

19 

1534 

3067 

4601 

6135 

1917 

3835 

5752 

7669 

20 

1883 

3766 

5649 

7532 

2354 

4708 

7062 

9416 

21 

2289 

4578 

6866 

9155 

2861 

5723 

8584 

11445 

22 

2757 

5514 

8271 

11028 

3446 

6893 

10339 

13786 

23 

3293 

6587 

9880 

13173 

4117 

8234 

12351 

16469 

24 

3905 

7809 

11714 

15618 

4881 

9763 

14644 

19525 

25 

4597 

9194 

13791 

18389 

5747 

11494 

17241 

22988 

26 

5378 

10756 

16134 

21512 

6723 

13447 

20170 

26893 

27 

6254 

12509 

18763 

25018 

7819 

15638 

23456 

31275 

28 

7234 

14467 

21701 

28935 

9043 

18086 

27129 

36173 

29 

8324 

16648 

24971 

33295 

10406 

20812 

31218 

41623 

30 

9533 

19065 

28598 

38131 

11917 

23834 

35751 

47669 

31 

10869 

21737 

32606 

43475 

13587 

27175 

40762 

54349 

32 

12340 

24681 

37021 

49362 

15427 

30854 

48282 

61709 

33 

13957 

27914 

41870 

55827 

17448 

34896 

52344 

69747 

34 

15727 

31454 

47181 

62908 

19661 

39322 

58983 

78643 

35 

17660 

35321 

52981 

70642 

22078 

44156 

66234 

88312 

36 

19767 

39534 

59301 

79068 

24711 

49423 

74134 

98845 

37 

22057 

44113 

66170 

88226 

27574 

55147 

82721 

110294 

38 

24539 

49079 

73618 

98158 

30678 

61355 

92033 

122710 

39 

27226 

54453 

81679 

108905 

34036 

68073 

102109 

136146 

40 

30128 

60256 

90384 

120512 

37664 

75328 

112992 

150656 

NOTE. — For  calculation  of  the  moment  of  inertia  the  bars  are  assumed  transformed  into  a  con- 
tinuous cylinder  having  a  sectional  area  equivalent  to  the  sum  of  the  area  of  the  bars. 


159 


CORRUGATED      BAR      COMPANY,      INC. 


A 


MOMENTS  OF  INERTIA  OF  BARS 

INCHES  4 

FOR  VARIOUS  DISTANCES  FROM  AN  Axis  A- A 
Values  Expressed  in  Nearest  Whole  Numbers 


Arm 

SQUARE  BARS 

ROUND  BARS 

in. 

K" 

%" 

H" 

Jr 

1* 

W% 

1M" 

fcF 

6A" 

%" 

w 

V 

1H" 

1^4 

2 

1 

2 

2 

3 

4 

5 

6 

1 

1 

2 

2 

3 

4 

5 

2J^ 

2 

2 

4 

5 

6 

8 

10 

1 

2 

3 

4 

5 

6 

8 

3 

2 

4 

5 

7 

9 

12 

14 

2 

3 

4 

5 

7 

9 

11 

3H 

3 

5 

7 

9 

12 

16 

19 

2 

4 

5 

7 

10 

12 

15 

4 

4 

6 

9 

12 

16 

20 

25 

3 

5 

7 

10 

13 

16 

20 

4^ 

5 

8 

11 

16 

20 

26 

32 

4 

6 

9 

12 

16 

20 

25 

5 

6 

10 

14 

19 

25 

32 

39 

5 

8 

11 

15 

20 

25 

31 

5J^ 

8 

12 

17 

23 

30 

38 

47 

6 

9 

13 

18 

24 

30 

37 

6 

9 

14 

20 

28 

36 

46 

56 

7 

11 

16 

22 

28 

36 

44 

6^ 

11 

17 

24 

32 

42 

54 

66 

8 

13 

19 

25 

33 

42 

52 

7 

12 

19 

28 

38 

49 

62 

77 

10 

15 

22 

29 

39 

•49 

60 

7H 

14 

22 

32 

43 

56 

71 

88 

11 

17 

25 

34 

44 

56 

69 

8 

16 

25 

36 

49 

64 

81 

100 

13 

20 

28 

39 

50 

64 

79 

8J-6 

18 

28 

41 

55 

72 

92 

113 

14 

22 

32 

43 

57 

72 

89 

9 

20 

32 

46 

62 

81 

103 

127 

16 

25 

36 

49 

64 

81 

100 

9^ 

23 

35 

51 

69 

90 

114 

141 

18 

28 

40 

54 

71 

90 

111 

10 

25 

39 

66 

77 

100 

127 

156 

20 

31 

44 

60 

79 

99 

123 

IOH 

28 

43 

62 

84 

110 

149 

172 

22 

34 

49 

66 

87 

110 

135 

11 

30 

47 

68 

93 

121 

153 

189 

24 

37 

53 

73 

95 

120 

149 

11^ 

33 

52 

74 

101 

132 

168 

207 

26 

41 

58 

80 

104 

132 

162 

12 

36 

56 

81 

110 

144 

182 

225 

28 

44 

64 

87 

113 

143 

177 

13 

42 

66 

95 

129 

169 

214 

264 

33 

52 

75 

102 

133 

168 

208 

14 

49 

77 

110 

150 

196 

248 

306 

38 

60 

87 

118 

154 

195 

241 

15 

56 

88 

127 

172 

225 

285 

352 

44 

69 

99 

135 

177 

224 

276 

16 

64 

100 

144 

196 

256 

324 

400 

50 

79 

113 

154 

201 

255 

314 

17 

72 

113 

163 

221 

289 

366 

452 

57 

89 

128 

174 

227 

287 

355 

18 

81 

127 

182 

248 

324 

410 

506 

64 

99 

143 

195 

255 

322 

398 

19 

90 

141 

203 

276 

361 

457 

564 

71 

111 

160 

217 

284 

359 

443 

20 

100 

156 

225 

306 

400 

506 

625 

79 

123 

177 

241 

314 

398 

491 

21 

110 

172 

248 

338 

441 

558 

689 

87 

135 

195 

265 

346 

438 

541 

22 

121 

189 

272 

371 

484 

613 

756 

95 

148 

214 

291 

380 

481 

594 

23 

132 

206 

298 

405 

529 

670 

827 

104 

162 

234 

318 

416 

526 

649 

24 

144 

225 

324 

441 

576 

729 

900 

113 

177 

254 

346 

452 

573 

707 

25 

156 

244 

352 

479 

625 

791 

977 

123 

192 

276 

376 

491 

621 

767 

26 

169 

264 

380 

518 

676 

856 

1056 

133 

207 

299 

407 

531 

672 

830 

27 

182 

285 

410 

558 

729 

923 

1139 

143 

224 

322 

438 

573 

725 

895 

28 

196 

306 

441 

600 

784 

992 

1225 

154 

241 

346 

471 

616 

779 

962 

29 

210 

329 

473 

644 

841 

1065 

1314 

165 

258 

372 

506 

661 

836 

1032 

30 

225 

352 

506 

689 

900 

1139 

1406 

177 

276 

398 

541 

707 

895 

1105 

32 

256 

400 

576 

784 

1024 

1296 

1600 

201 

314 

452 

616 

804 

1018 

1257 

34 

289 

452 

650 

885 

1156 

1463 

1806 

227 

355 

511 

695 

908 

1149 

1419 

36 

324 

506 

729 

992 

1296 

1640 

2025 

254 

398 

573 

779 

1018 

1288 

1591 

38 

361 

564 

812 

1106 

1444 

1828 

2256 

283 

443 

638 

868 

1134 

1435 

1772 

40 

400 

625 

900 

1225 

1600 

2025 

2500 

314 

491 

707 

962 

1257 

1590 

1964 

42 

441 

689 

992 

1351 

1764 

2233 

2756 

346 

541 

779 

1061 

1385 

1753 

2165 

44 

484 

756 

1089 

1482 

1936 

2450 

3025 

380 

594 

855 

1164 

1521 

1924 

2376 

46 

529 

827 

1190 

1620 

2116 

2678 

3306 

415 

649 

935 

1272 

1662 

2103 

2597 

48 

576 

900 

1296 

1764 

2304 

2916 

3600 

452 

707  1018 

1385 

1810 

2290 

2828 

160 


USEFUL      DATA 


Beam 
Quantities 


BEAM  QUANTITIES 

CUBIC  FEET  OF  CONCRETE  PER  LINEAR  FOOT  OF  BEAM 


Depth 

WIDTH  IN  INCHES 

in. 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

6 

0.17 

0.21 

0.25 

0.29 

0.33 

0.38 

0.42 

0.46 

0.50 

0.54 

0.58 

0.63 

0.67 

0.71 

0.75 

7 

0.19 

0.24 

0.29 

0.34 

0.39 

0.44 

0.49 

0.53 

0.58 

0.63 

0.68 

0.73 

0.78 

0.83 

0.88 

8 

0.22 

0.28 

0.33 

0.39 

0.44 

0.50 

0.56 

0.61 

0.67 

0.72 

0.78 

0.83 

0.89 

0.94 

1.00 

9 

0.25 

0.31 

0.38 

0.44 

0.50 

0.56 

0.63 

0.69 

0.75 

0.81 

0.88 

0.94 

1.00 

1.06 

1.13 

10 

0.28 

0.35 

0.42 

0.49 

0.56 

0.63 

0.69 

0.76 

0.83 

0.90 

0.97 

1.04 

1.11 

1.18 

1.25 

11 

0.31 

0.38 

0.46 

0.53 

0.61 

0.69 

0.76 

0.84 

0.92 

0.99 

.07 

1.15 

1.22 

.30 

1.38 

12 

0.33 

0.42 

0.50 

0.58 

0.67 

0.75 

0.83 

0.92 

1.00 

1.08 

.17 

1.25 

1.33 

.42 

1.50 

13 

0.36 

0.45 

0.54 

0.63 

0.72 

0.81 

0.90 

0.99 

1.08 

1.17 

.26 

1.35 

1.44 

.53 

1.63 

14 

0.39 

0.49 

0.58 

0.68 

0.78 

0.88 

0.97 

1.07 

1.17 

1.26 

.36 

1.46 

1.56 

.65 

1.75 

15 

0.42 

0.52 

0.63 

0.73 

0.83 

0.94 

1.04 

1.15 

1.25 

1.35 

.46 

1.56 

1.67 

.77 

1.88 

16 

0.44 

0.56 

0.67 

0.78 

0.89 

1.00 

1.11 

1.22 

1.33 

1.44 

.56 

1.67 

1.78 

1.89 

2.00 

17 

0.47 

0.59 

0.71 

0.83 

0.94 

1.06 

1.18 

1  30 

1.42 

1.54 

.65 

1.77 

1.89 

2.01 

2.13 

18 

0.50 

0.63 

0.75 

0.88 

1.00 

1.13 

1.25 

1.38 

1.50 

1.63 

.75 

1.88 

2.00 

2.13 

2.25 

19 

0.53 

0.66 

0.79 

0.92 

1.06 

1.19 

1.32 

1.45 

1.58 

1.72 

.85 

1.98 

2.11 

2.24 

2.38 

20 

0.56 

0.69 

0.83 

0.97 

1.11 

1.25 

1.39 

1.53 

1.67 

1.81 

.94 

2.08 

2.22 

2.36 

2.50 

21 

0.58 

0.73 

0.88 

1.02 

1.17 

1.31 

1.46 

1.60 

1.75 

1.90 

2.04 

2.19 

2.33 

2.48 

2.63 

22 

0.61 

0.76 

0.92 

1.07 

1.22 

1.38 

1.53 

1.68 

1.83 

1.99 

2.14 

2.29 

2.44 

2.60 

2.75 

23 

0.64 

0.80 

0.96 

1.12 

1.28 

1.44 

1.60 

1.76 

1.92 

2.08 

2.24 

2.40 

2.56 

2.72 

2.88 

24 

0.67 

0.83 

1.00 

1.17 

1.33 

1.50 

1.67 

1.83 

2.00 

2.17 

2.33 

2.50 

2.67 

2.83 

3.00 

25 

0.69 

0.87 

1.04 

1.22 

1.39 

1.56 

1.74 

1.91 

2.08 

2.26 

2.43 

2.60 

2.78 

2.95 

3.13 

26 

0.72 

0.90 

1.08 

1.26 

1.44 

1.63 

1.81 

1.99 

2.17 

2.35 

2.53 

2.71 

2.89 

3.07 

3.25 

27 

0.75 

0.94 

1.13 

1.31 

1.50 

1.69 

1.88 

2.06 

2.25 

2.44 

2.63 

2.81 

3.00 

3.19 

3.38 

28 

0.78 

0.97 

1.17 

1.36 

1.56 

1.75 

1.94 

2.14 

2.33 

2.53 

2.72 

2.92 

3.11 

3.31 

3.50 

29 

0.81 

1.01 

1.21 

1.41 

1.61 

1.81 

2.01 

2.22 

2.42 

2.62 

2.82 

3.02 

3.22 

3.42 

3.62 

30 

0.83 

1.04 

1.25 

1.46 

1.67 

1.88 

2.08 

2.29 

2.50 

2.71 

2.92 

3.13 

3.33 

3.54 

3.75 

31 

0.86 

1.08 

1.29 

1.51 

.72 

1.94 

2.15 

2.37 

2.58 

2.80 

3.01 

3.23 

3.44 

3.66 

3.88 

32    !0.89 

1.11 

1.33 

1.56 

.78 

2.00 

2.22 

2.44 

2.67 

2.89 

3.11 

3.33 

3.56 

3.78 

4.00 

33 

0.92 

1.15 

1.38 

1.60 

.83 

2.06 

2.29 

2.52 

2.75 

2.98 

3.21 

3.44 

3.67 

3.90 

4.13 

34 

0.94 

1.18 

1.42 

1.65 

.89 

2.13 

2.36 

2.60 

2.83 

3.07 

3.31 

3.54 

3.78 

4.01 

4.25 

35 

0.97 

1.22 

1.46 

1.70 

.94 

2.19 

2.43 

2.67 

2.92 

3.16 

3.40 

3.65 

3.89 

4.13 

4.38 

36 

1.00 

1.25 

1.50 

1.75 

2.00 

2.25 

2.50 

2.75 

3.00 

3.25 

3.50 

3.75 

4.00 

4.25 

4.50 

37 

1.03 

1.28 

1.54 

1.80 

2.06 

2.31 

2.57 

2.83 

3.08 

3.34 

3.60 

3.85 

4.11 

4.37 

4.63 

38 

1.06 

1.32 

1.58 

1.85 

2.11 

2.38 

2.64 

2.90 

3.17 

3.43 

3.69 

3.96 

4.22 

4.49 

4.75 

39 

1.08 

1.35 

1.63 

1.90 

2.17 

2.44 

2.71 

2.98 

3.25 

3.52 

3.79 

4.06 

4.33 

4.60 

4.88 

40 

1.11 

1.39 

1.67 

1.94 

2.22 

2.50 

2.78 

3.06 

3.34 

3.61 

3.89 

4.17 

4.45 

4.72 

5.00 

41 

1.14 

1.42 

1.71 

1.99 

2.28 

2.56 

•2.85 

3.13 

3.42 

3.70 

3.99 

4.27 

4.55 

4.84 

5.12 

42 

1.17 

1.46 

1.75 

2.04 

2.33 

2.63 

2.92 

3.21 

3.50 

3.79 

4.08 

4.38 

4.67 

4.96 

5.25 

43 

.19 

.49 

1.79 

2.09 

2.39 

2.69 

2.99 

3.28 

3.58 

3.88 

4.18 

4.48 

4.78 

5.08 

5.38 

44 

.22 

.53 

1.83 

2.14 

2.44 

2.75 

3.06 

3.36 

3.67 

3.97 

4.27 

4.58 

4.89 

5.19 

5.50 

45 

.25 

.56 

1.88 

2.19 

2.50 

2.81 

3.13 

3.44 

3.75 

4.06 

4.38 

4.69 

5.00 

5.31 

5.63 

46 

.28 

.60 

1.92 

2.24 

2.56 

2.88 

3.19 

3.51 

3.83 

4.15 

4.47 

4.79 

5.11 

5.43 

5.75 

47 

1.31 

.63 

1.96 

2.28 

2.61 

2.94 

3.26 

3.59 

3.92 

4.24 

4.57 

4.90 

5.22 

5.55 

5.88 

48 

.33 

.67 

2.00 

2.33 

2.67 

3.00 

3.33 

3.67 

4.00 

4.33 

4.67 

5.00 

5.33 

5.67 

6  00 

161 


Column 

Head 

Quantities 


CORRUGATED      BAR      COMPANY,     INC. 


1       2      3       4      5      6       7      8       9      10     11     12     13     14     15     16     17     18     19     20 
Cubic  Feet  of  Concrete  in  Head  when  Angle  is  45° 


1     | 


|    I    I    I     I    |    I    I    I    I    I    I    I    I    I    |    I     I    i    i    |    !    I    I     I    I    I    I 
0  5  10  15  20  25  30  35 

Cubic  Feet  of  Concrete  in  Head  when  Angle  is  30° 

The  above  diagram  gives  the  volume  of  the  ring  of  concrete  forming  the  head.  Volumes  given 
are  for  octagonal  heads  and  columns.  For  square  heads  and  columns  multiply  the  volume  by  1.21 
For  round  heads  and  columns  multiply  the  volume  by  0.95. 

DIAGRAM  17 

For  obtaining  volume  of  concrete  in  column  heads  of  columns 
supporting  flat  slab  floors. 


162 


USEFUL      DATA 

QUANTITIES  OF  MATERIALS  FOR  ONE    CUBIC  YARD  OF    RAMMED 
CONCRETE  BASED  ON  A  BARREL  OF  3.8  CUBIC  FEET 

The  following  table  gives  the  quantities  of  materials  required  for  one  yard  of  concrete.  The  results  given 
have  been  taken  from  a  similar  table  in  Concrete  Plain  and  Reinforced  by  Taylor  and  Thompson,  with 
the  author's  permission,  to  use  this  copyrighted  matter. 


"oportions 

Proportions 

PERCENTAGES  OP  VOIDS  IN  BROKEN  STONE  OR  GRAVEL 

by 

by 

50%  Broken 

45% 

40% 

30% 

Parts 

Volumes 

Stone  Screened 

Average 

Gravel  or 

Graded 

to  Uniform  size 

Condition 

Mixed 

Mixtures 

v  §  i    •_ 
MX  ;    03-0 

§a 

m 

- 

§ 

1 

•0 

§ 

•• 
a 

8 

I 

"C 

• 

QJ 

S§    §9 

§3 

5 

s 

o 

§ 

§ 

o 

§ 

o 

3 

• 

o 

*O 

g 

fcO 

M)£ 

t-502 

0 

02 

OQ 

O 

02 

02 

O 

02 

02 

O 

02 

02 

Bbl. 

Cu.  Ft. 

Cu.Ft. 

Bbl. 

Cu  Yd 

Cu.Yd 

Bbl. 

Cu-Yd. 

Cu.Yd. 

Bbl. 

Cu.Yd. 

Cu.Yd. 

Bbl. 

Cu.Yd. 

Cu.Yd. 

1 

1.5 

1 

3.8 

5.7 

3.19 

0.45 

0.67 

3.08 

0.43 

0.65 

2.97 

0.42 

0.63 

2.78 

0.39 

0.59 

2 

1 

3.8 

7.6 

2.85 

0.40 

0.80 

2.73 

0.38 

0.77 

2.62 

0.37 

0.74 

2.43 

0.34 

0.68 

2.5 

3.8 

9.5 

2.57 

0.36 

0.90 

2.45 

0.34 

0.86 

2.34 

0.33 

0.82 

2.15 

0.30 

0.76 

3 

3.8 

11.4 

2.34 

0.33 

0.99 

2.22 

0.31 

0.94 

2.12 

0.30 

0.90 

1.93 

0.27 

0.82 

.5 

2 

5.7 

7.6 

2.49 

0.53 

0.70 

2.40 

0.51 

0.68 

2.31 

0.49 

0.65 

2.16 

0.46 

0.61 

.5 

2.5 

5.7 

9.5 

2.27 

0.48 

0.80 

2.18 

0.46 

0.77 

2.09 

0.44 

0.74 

1.94 

0.41 

0.68 

.5 

3 

5.7 

11.4 

2.09 

0.44 

0.88 

2.00 

0.42 

0.84 

1.91 

0.40 

0.81 

1.76 

0.37 

0.74 

.5 

3.5 

5.7 

13.3 

1.94 

0.41 

0.96 

1.84 

0.39 

0.91 

1.76 

0.37 

0.87 

1.61 

0.34 

0.79 

.5 

4 

5.7 

15.2 

1.80 

0.38 

1.01 

1.71 

0.36 

0.96 

1.63 

0.34 

0.92 

1.48 

0.31 

0.83 

1.5 

4.5 

5.7 

17.1 

1.69 

0.36 

1.07 

1.60 

0.34 

1.01 

1.51 

0.22 

0.96 

1.37 

0.29 

0.87 

1.5 

5 

5.7 

19.0 

1.59 

0.34 

1.12 

1.50 

0.32 

1.06 

1.42 

0.30 

1.00 

1.28 

0.27 

0.90 

2 

3 

7.6 

11.4 

1.89 

0.53 

0.80 

1.81 

0.51 

0.76 

1.74 

0.49 

0.74 

1.61 

0.45 

0.68 

2 

3.5 

7.6 

13.3 

1.76 

0.49 

0.87 

1.68 

0.47 

0.83 

1.61 

0.45 

0.79 

1.48 

0.42 

0.73 

2 

4 

7.6 

15.2 

1.65 

0.46 

0.93 

1.57 

0.44 

0.88 

1.50 

0.42 

0.84 

.38 

0.39 

0.78 

2 

4.5 

7.6 

17.1 

1.55 

0.44 

0.98 

1.48 

0.42 

0.94 

1.41 

0.40 

0.89 

.28 

0.36 

0.81 

2 

5 

7.6 

19.0 

1.47 

0.41 

1.03 

1.39 

0.39 

0.98 

1.32 

0.37 

0.93 

.20 

0.34 

0.84 

2 

5.5 

7.6 

20.9 

1.39 

0.39 

1.08 

1.31 

0.37 

1.01 

1.25 

0.35 

0.97 

.13 

0.32 

0.87 

2       6 

7.6 

22.8 

1.32 

0.37 

1.11 

1.25 

0.35 

1.06 

1.18 

0.33 

1.00 

.06 

0.30 

0.89 

2.5   3 

9.5 

11.4 

1.72 

0.61 

0.73 

1.66 

0.58 

0.70 

1.60 

0.56 

0.68 

.49 

0.52 

0.63 

2.5   3.5 

9.5 

13.3 

1.62 

0.57 

0.80 

1.55 

0.55 

0.76 

1.49 

0.52 

0.73 

.38 

0.49 

0.68 

2.5)  4 

9.5 

15.2 

1.52 

0.54 

0.86 

1.46 

0.51 

0.82 

1.40 

0.49 

0.79 

.29 

0.45 

0.73 

2.5   4.5 

9.5 

17.1 

1.44 

0.51 

0.91 

1.37 

0.48 

0.87 

1.31 

0.46 

0.83 

.20 

0.42 

0.76 

2.5   5 

9.5 

19.0 

1.37 

0.48 

0.96 

1.30 

0.46 

0.92 

1.24 

0.44 

0.87 

.13 

0.40 

0.80 

2.5    5.5 

1 

9.5 

20.9 

1.30 

0.46 

1.01 

1.23 

0.43 

0.95 

1.17 

0.41 

0.91 

.07 

0.38 

0.83 

2.5 

6 

1 

9.5 

22.8 

1.24 

0.44 

1.05 

1.17 

0.41 

0.99 

1.11 

0.39 

0.94 

1.01 

0.36 

0.85 

2.5 

6.5 

1 

9  5 

24  7 

1   18 

0  42 

1  08 

1.12 

0.39 

1.02 

1  06 

0  37 

0  97 

0  96 

0.34 

0.88 

2.5 

7 

1 

9.5 

26.6 

1.13 

0.40 

1.11 

1.07 

0.38 

1.05 

1.01 

0.36 

0.99 

0.91 

0.32 

0.90 

3 

4 

11.4 

15.2 

1.42 

0.60 

0.80 

1.36 

0.57 

0.77 

1.30 

0.55 

0.73 

1.21 

0.51 

0.68 

3 

4.5 

11.4 

17.1 

1.34 

0.57 

0.85 

1.28 

0.54 

0.81 

1.23 

0.52 

0.78 

1.13 

0.48 

0.72 

3 

5 

11.4 

19.0 

1.28 

0.54 

0.90 

1.22 

0.52 

0.86 

1.17 

0.49 

0.82 

1.07 

0.45 

0.75 

3 

5.5 

11.4 

20.9 

1.22 

0.52 

0.94 

1.16 

0.49 

0.90 

1.11 

0.47 

0.86 

1.01 

0.43 

0.78 

3 

6 

11.4 

22.8 

1.16 

0.49 

0.98 

1.11 

0.47 

0.94 

1.05 

0.44 

0.89 

0.96 

0.41 

0.81 

3 

6.5 

11.4 

24.7 

1.12 

0.47 

1.02 

1.06 

0.45 

0.97 

1.01 

0.43 

0.92 

0.92 

0.39 

0.84 

3 

7 

11.4 

26.6 

1.07 

0.45 

1.05 

1.01 

0.43 

0.99 

0.96 

0.40 

0.95 

0.87 

0.37 

0.86 

3 

7.5 

11.4 

28.5 

1.03 

0.44 

1.09 

0.97 

0.41 

1.02 

0.92 

0.39 

0.97 

0.83 

0.35 

0.88 

3 

8 

11.4 

30.4 

0.99 

0.42 

1.11 

0.93 

0.39 

1.05 

0.88 

0.37 

0.99 

0.80 

0.34 

0.90 

4 

5 

15.2 

19.0 

1.13 

0.64 

0.80 

1.08 

0.61 

0.76 

1.04 

0.59 

0.73 

0.96 

0.54 

0.68 

4 

6 

15.2 

22.8 

1.04 

0.59 

0.88 

0.99 

0.56 

0.84 

0.95 

0.54 

0.80 

0.87 

0.49 

0.73 

4 

7 

15.2 

26.6 

0.96 

0.54 

0.95 

0.92 

0.52 

0.91 

0.88 

0.50 

0.87 

0.80 

0.45 

0.79 

4 

8 

15.2 

30.4 

0.90 

0.51 

1.01 

0.85 

0.48 

0.96 

0.81 

0.46 

0.91 

0.74 

0.42 

0.83 

4 

9 

15.2 

34.2 

0.84 

0.47 

1.06 

0.80 

0.45 

1.01 

0.76 

0.43 

0.96 

0.68 

0.38 

0.86 

4 

10 

15.2 

38.0 

0.79 

0.44 

1.11 

0.75 

0.42 

1.06 

0.71 

0.40 

1.00 

0.64 

0.36 

0.90 

5 

10 

19.0 

38.0 

0.73 

0.52 

1.03 

0.69 

0.49 

0.97 

0.66 

0.46 

0.93 

0.60 

0.42 

0.84 

6 

12 

1 

22.8 

45.5 

0.62 

0.52 

1.04 

0.58 

0.49 

0.98 

0.56 

0.47 

0.94 

0.50 

0.42 

0.84 

NOTE. — Variations  In  the  fineness  of  the  sand  and  the  compacting  of  the  concrete  may  affect  the  qi 
titles  by  10%  in  either  direction. 

Use  45%  column  for  average  conditions  and  for  broken  stone  with  dnst  screened  out. 
Use  50%  column  for  broken  stone  screened  to  uniform  size 
Use  40%  column  for  gravel  or  mixed  stone  and  gravel. 
Use  30%  column  for  scientifically  graded  mixtures. 


163 


CORRUGATED   BAR   COMPANY,  INC. 


BARS 

One  of  the  assumptions  always  made  in  connection  with  the  design  of  reinforced 
concrete  structures  is  that  the  steel  and  concrete  are  so  intimately  united  by  means 
of  the  bond  that  the  two  materials  act  together  as  a  single  new  material.  For  many 
years  it  was  insisted  upon  that  the  adhesion  between  concrete  and  plain  bars  was 
sufficient,  but  as  the  art  of  reinforced  concrete  construction  developed  the  sufficiency  of 
this  adhesion  began  to  be  questioned  and  various  methods  were  devised,  such  as  hook- 
ing or  splitting  the  ends  of  the  bars,  to  prevent  their  slipping  in  the  concrete.  Such 
methods  are  but  makeshifts  at  best,  as  bond  to  be  effective  must  be  continuous,  and  in 
practically  all  reinforced  concrete  designs  of  to-day  the  demand  is  for  a  deformed 
bar  of  proper  design — a  bar  that  grips  the  concrete  in  a  positive  manner  by  means 
of  projecting  ribs  normal  to  the  direction  of  stress. 

The  design  tables  appearing  in  this  book  are  based  on  the  employment  of  a  properly 
designed  deformed  bar,  and  their  use  in  connection  with  other  types  of  bars  is  not 
recommended. 


CORRUGATED  ROUNDS 


STANDARD  SIZES 


SIZE  IN  INCHES  

% 

H 

*A 

3A 

« 

1 

IH 

m 

Net  Area  in  Square  Inches  . 
Weight  per  Foot  in  Pounds  . 
Perimeter  in  Inches  .  .  . 

0.11 
0.38 
1.23 

0.19 
0.66 
1.66 

0.30 
1.05 
2.10 

0.44 
1.52 
2.53 

0.60 
2.06 
2.95 

0.78 
2.69 
3.36 

0.99 
3.41 
3.80 

1.22 
4.21 
4.23 

CORRUGATED  SQUARES 


STANDARD  SIZES 


SIZE  IN  INCHES  

y* 

X 

y2 

K 

H 

H 

1 

1H 

1M 

Net  Area  in  Square  Inches  . 
Weight  per  Foot  in  Pounds  . 
Perimeter  in  Inches  .  .  . 

0.06 
0.22 
1.00 

0.14 
0.49 
1.50 

0.25 
0.86 
2.00 

0  39 
1.35 
2.50 

0.56 
1.94 
3.00 

0.76 
2.64 
3.50 

1.00 
3.43 
4.00 

1.26 
4.34 
4.50 

1.55 
5.35 
5.00 

164 


USEFUL      DATA 


Specifications.  Purchasers  can  greatly  influence  the  prompt  shipment  of  orders 
for  ordinary  "mill  shipment"  by  considering,  in  the  preparation  of  their  specifications 
and  material  bills,  the  factors  connected  with  the  methods  and  internal  organization 
of  a  steel  mill. 

Adherence  to  the  Manufacturers'  Standard  Specifications  for  Defornled  Concrete 
Reinforcing  Bars  (see  page  188),  will  always  facilitate  prompt  shipment.  It  is,  of 
course,  possible  to  furnish  any  class  of  material  that  is  within  the  power  of  the  mill  to 
roll,  but  where  specifications  are  in  any  way  special  the  entire  order  must  be 
made  from  special  heats.  The  process  is  one  out  of  the  ordinary  routine  of  the 
mill,  billets  already  prepared  cannot  be  used,  and  delay  in  the  filling  of  the  order 
is  certain. 

Sizes.  It  is  necessary  in  the  rolling  of  steel  bars,  for  a  mill  to  finish  rolling  all  of 
the  bars  on  its  schedule  of  one  particular  size  before  changing  the  rolls  for  other  sizes 
of  bars.  In  mill  parlance,  what  is  known  as  a  "rolling"  extends  over  a  period  of  several 
days  and  an  order  containing  a  large  number  of  sizes  might  be  compelled  to 
remain  in  the  mill  until  the  completion  of  the  entire  rolling,  so  that  where  quick 
shipment  is  desired,  the  number  of  sizes  on  an  order  should  be  kept  as  low  as 
possible. 

In  addition  to  confining  the  order  to  as  few  sizes  as  may  be  consistent  with  the 
requirements,  every  endeavor  should  be  made  to  avoid  specifying  bars  in  r^th  sizes. 
This  is  an  error  frequently  made  by  inexperienced  designers  in  an  effort  to  meet  a 
theoretical  steel  area  required  by  their  calculations,  and  can  only  result  in  delay  at 
the  mill  and  increased  labor  and  confusion  in  the  field  through  the  necessity  of  handling 
a  multiplicity  of  bars  of  slightly  varying  size. 

Lengths.  In  ordinary  mill  practice  the  bars  are  rolled  to  lengths  varying  from 
100  to  300  feet  and  sheared  into  lengths  called  for  by  the  material  bills  as  they  come 
from  the  rolls.  When,  however,  the  number  of  lengths  are  very  large  and  where  there 
are  only  a  small  number  of  bars  of  one  length,  the  shearing  cannot  be  done  as  fast  as 
the  bars  are  rolled,  consequently  the  bars  must  be  laid  to  one  side  and  sheared 
after  the  conclusion  of  the  rolling  in  order  that  the  operation  of  the  mill  may  not  be 
delayed.  It  is,  therefore,  always  desirable  to  keep  the  number  of  lengths  as  low  as 
possible  where  quick  shipment  is  a  necessary  requirement. 

The  lengths  should  always  be  given  to  the  nearest  inch  as  bars  are  not  ordinarily 
sheared  to  a  greater  degree  of  accuracy.  Where  it  is  important  that  the  length 
called  for  be  exact,  a  note  to  this  effect  should  be  placed  opposite  the  item  on  the 
order. 

Fabrication.  For  all  reinforced  concrete  structures  there  is  usually  a  considerable 
amount  of  fabricated  reinforcement  to  be  furnished.  Sometimes  this  fabrication  is 
done  in  the  field  but  through  the  use  of  special  machinery  and  methods  of  operation 
all  classes  of  bending  and  other  fabrication  of  bar  reinforcement  can  be  accomplished 
with  greater  accuracy  and  advantage  in  the  shop  than  in  the  field,  and  in  the 
majority  of  instances  it  is  advisable  for  the  purchaser  to  specify  "shop  fabrica- 
tion." 

Accompanying  all  orders  for  fabricated  material  there  should  be  furnished  in  addi- 
tion to  the  list  of  number  of  pieces,  size  and  length  of-  bar,  a  sketch  of  each  differently 
fabricated  piece  with  the  dimensions  plainly  marked  thereon.  A  few  of  the  details 

165 


CORRUGATED      BAR      COMPANY,     INC. 


most  frequently  encountered  in  practice  are  given  below,  showing  in  each  case  the 
detail  dimensions  required  by  the  shop. 


1-1 

X, 

v 

inside 


Lap 


inside 


166 


USEFUL      DATA 


Wire 


AMERICAN  STEEL  AND  WIRE  CO.'S  STEEL  AND  IRON  WIRE  GAUGE 
AND   DIFFERENT  SIZES  OF  WIRE 


Diameter 
Inches 

Steel  Wire 
Gauge 

Diameter 
Inches 

Area,  Square 
Inches 

Pounds 
per  Foot 

Feet 
per  Pound 

Feet  per 
2,000  Lbs. 

H 

0.500 

0.19635 

0.6625 

1.50 

3018 

* 

0.490         0.18857 

0.6363 

1.51 

3023 

H 

0.468         0.17202 

0.5804 

1.72 

3445 

I 

0.460         0.16619 

0.5608 

1.78 

3566 

ft 

0.437 

0.14998 

0.5061 

1.97 

3952 

* 

0.430 

0.14532 

0.4901 

2.04 

4081 

3L! 

0.406 

0.12946 

0.4368 

2.28 

4578 

* 

0.393  . 

0.12130 

0.4094 

2.44 

4885 

N 

0.375 

0.11044 

0.3726 

2.68 

5367 

f 

0.362 

0.10292 

0.3473 

2.87 

5758 

H 

0.343 

0.09240 

0.3117 

3.20 

6412 

I 

0.331 

0.08604 

0.2904 

3.44 

6887 

A 

0.312 

0.07645 

0.2579 

3.87 

7755 

0 

0.307 

0.07402 

0.2497 

4.00 

8011 

1 

0.283 

0.06290 

0.2123 

4.71 

9420 

A 

0.281 

0.06210 

0.2092 

4.78 

9560 

2 

0.263 

0.05432 

0.1834 

5.45 

10905 

M 

0.250 

0.04908 

0.1656 

6.03 

12077 

3 

0.244 

0.04675 

0.1578 

6.33 

12674 

4 

0.225 

0.03976 

0.1342 

7.45 

14903 

A 

0.218 

0.03732 

0.1259 

7.94 

15885 

5 

0.207 

0.03365 

0.1135 

8.81 

17621 

6 

0.192 

0.02895 

0.0977 

10.23            20471 

A 

0.187 

0.02746 

0.0926 

10.79            21598 

7 

0.177      i    0.02460 

0.0830 

12.04            24096 

8 

0.162 

0.02061 

0.0696 

14.36 

28735 

A 

0.156 

0.01911 

0.0644 

15.52            31056 

9 

0.148 

0.01720 

0.0580 

17.24 

34482 

10 

0.135 

0.01431 

0.0483 

20.70 

41408 

H 

0.125 

0.01227 

0.0414 

24.15            48309 

11 

0.120 

0.01130 

0.0382 

26.17            52356 

12 

0.105 

0.00865 

0.0292 

34.24            68493 

A 

0.093 

0.00679 

0.0229 

43.66            87336 

13 

0.092 

0.00664 

0.0224 

44.64            89286 

14 

0.080 

0.00502 

0.0169 

59.17           118343 

15 

0.072 

0.00407 

0.0137 

72.99           145985 

16 

0.063 

0.00311 

0.0105 

95.23           190476 

167 


CORRUGATED   BAR   COMPANY,  INC. 


IICO 

!> 


I* •« * 


168 


USEFUL      DATA 


Properti 

of 

Sections 


gs 

y    2 
I    I 

IB 

Q  < 


Sis 


169 


CORRUGATED   BAR   COMPANY,  INC. 


Sis 


•« 

'^ 


P? 


SI 


I 


?? 


"•"£•£» 


170 


USEFUL      DATA 


^   o 


I! 
I 

Q  <J 


171 


Timber 


CORRUGATED      BAR      COMPANY,     INC. 


TIMBER 

UNIT  STRESSES  IN  POUNDS  PER  SQUARE  INCH  AND  WEIGHTS  PER  CUBIC  FOOT* 


White 
Oak 

Western 
Hemlock 

Spruce 

Norway 
Pine 

Shortleaf 
Pine 

Longleaf 
Pine 

Douglas 
Fir 

EXTREME  FIBRE  STRESS 

Ultimate    .... 

5,700 

5,800 

4,800 

4,200 

5,600 

6,500 

6,100 

1 

Working  Stress     . 

1,100 

1,100 

1,000 

800 

1,100 

1,300 

1,200 

H 
pq 

MODULUS  OF  ELAS- 

— 

TICITY 
'  Average     .... 

1,150,000 

1,480,000 

1,310000 

1,190,000 

1,480,000 

1,610,000 

1,510,000 

PARALLEL  TO  GRAIN 

Ultimate    .... 

840 

630 

600 

590 

710 

720 

690 

SHEARING 

Working  Stress     . 

LONGITUDINAL  SHEAR 
IN  BEAMS 

210 

160 

150 

130 

170 

180 

170 

Ultimate    .... 

270 

270 

170 

250 

330 

300 

270 

Working  Stress     . 

110 

100 

70 

100 

130 

120 

110 

PERPENDICULAR  TO 

GRAIN 

Elastic  Limit    .    . 

920 

440 

370 

300 

340 

520 

630 

Working  Stress     . 

460 

220 

180 

150 

170 

260 

310 

. 

PARALLEL  TO  GRAIN 

1 

Ultimate    .... 

3,500 

3,500 

3,200 

2,600 

3,400 

3,800 

3,600 

o 

Working  Stress     . 

1,300 

1,200 

1,100 

800 

1,100 

1,300 

1,200 

WORKING   STRESSES 

FOR  COLUMNS 

l/d  less  than  15    . 

975 

900 

825 

600 

825 

975 

900 

l/d  more  than  15  . 

1,300(1- 

Z/60d) 

1,200(1- 
J/60d) 

1,100(1- 
Z/60d) 

800(1- 
Z/60d) 

1,100(1- 
Z/60d) 

1,300(1- 
Z/60d) 

1,200(1- 
Z/60d) 

Weight  per  cu.  ft.  (green) 

pounds     

48 

41 

33 

42 

50 

50 

38 

W( 
I 

ight  per  cu.  ft.  (dry) 
>ounds         

43 

27 

27 

32 

36 

40 

32 

The  stresses  given  are  for  green  timber.     For  temporary  structures  an  increase  of  50%  in  the 
working  stresses  is  permissible. 

*Unit  stresses  adopted  by  The  Am.  Ry.  Eng.  Asso.  for  railroad  structures. 


172 


USEFUL      DATA 


Timber 


WOODEN  BEAMS— UNIFORMLY  LOADED 

Loads  given  are  total  loads  for  a  beam  one  inch  thick  and  for  a  maximum  bending  stress  of  1,000 
pounds  per  square  inch. 


Span 
in 
Feet 

DEPTH  OP  BEAM  IN  INCHES 

2 

4 

6 

8 

10 

12     14 

16 

18 

20 

2 

187 

3 

148 

4 

111 

5 

89 

356 

6 

74 

296 

7 

63 

254 

8 

56 

222 

500 

9 

198 

444 

10 

178 

400 

711 

11 

162 

364 

646 

12 

148 

333 

593 

926 

13 

308 

547 

855 

14 

286 

508 

794 

15 

267 

474 

741 

1067 

16 

250 

444 

694 

1000 

17 

418 

654 

941 

1281 

18 

395 

617 

889 

1210 

19 

374 

585 

842 

1146 

20 

356 

556 

800 

1089 

1422 

21 

529 

762 

1037 

1354 

22 

505 

727 

990 

1293 

1636 

23 

483 

696 

947 

1237 

1565 

24 

463 

667 

907 

1185 

1500 

1852 

25 

640 

871 

1138 

1440 

1778 

SQUARE  WOODEN  COLUMNS 

Loads  given  are  in  thousands  of  pounds  for  a  working  stress  parallel  to  the  grain  of  1,000  pounds 
per  square  inch. 

p=i,ooo(i-  yL 


Height 
of 
Column 

SIDE  OP  SQUARE  IN  INCHES 

4 

6 

8 

10 

12 

14 

16 

18 

20 

24 

5 

12.0 

27.0 

48.0 

75.0 

108.0 

147.0 

192.0 

243.0 

300.0 

432.0 

6 

11.2 

27.0 

48.0 

75.0 

108.0 

147.0 

192.0 

243.0 

300.0 

432.0 

7 

10.4 

27.0 

48.0 

75.0 

108.0 

147.0 

192.0 

243.0 

300.0 

432.0 

8 

9.6 

26.4 

48.0 

75.0 

108.0 

147.0 

192.0 

243.0 

300.0 

432.0 

9 

8.8 

25.2 

48.0 

75.0 

108.0 

147.0 

192.0 

243.0 

300.0 

432.0 

10 

8.0 

24.0 

48.0 

75.0 

108.0 

147.0 

192.0 

243.0 

300.0 

432.0 

11 

22.8 

46.4 

75.0 

108.0 

147.0 

192.0 

243.0 

300.0 

432.0 

12 

21.6 

44.8 

75.0 

108.0 

147.0 

192.0 

243.0 

300.0 

432.0 

14 

19.2 

41.6 

72.0 

108.0 

147.0 

192.0 

243.0 

300.0 

432.0 

16 

38.4 

68.0 

105.6 

147.0 

192.0 

243.0 

300.0 

432.0 

18 

35.2 

64.0 

100.8 

145.6 

192.0 

243.0 

300.0 

432.0 

20 

32.0 

60.0 

96.0 

140.0 

192.0 

243.0 

300.0 

432.0 

To  obtain  the  carrying  capacity  of  beams  or  columns  where  the  unit  stress 
pounds  per  square  inch,  increase  or  decrease  the  table  loads  proportionately. 


unit  stress  is  other  than  1,000 


173 


CORRUGATED   BAR   COMPANY,  INC. 


AREAS  OF  CIRCULAR  SEGMENTS 

FOR  RATIOS  OF  RISE  AND  CHORD 


Area  =  CxR  x  Coefficient 


A° 

Coeffi- 
cient 

R 
C 

A° 

Coeffi- 
cient 

R 
C 

A° 

Coeffi- 
cient 

R 
C 

A° 

Coeffi- 
cient 

R 

C 

1 

0.6667 

0.0022 

46 

0.6722 

0.1017 

91 

0.6895 

0.2097 

136 

0.7239 

0.3373 

2 

0.6667 

0  .  0044 

47 

0.6724 

0  .  1040 

92 

0.6901 

0.2122 

137 

0.7249 

0.3404 

3 

0.6667 

0  .  0066 

48 

0.6727 

0  .  1063 

93 

0.6906 

0.2148 

138 

0.7260 

0.3436 

4 

0.6667 

0.0087 

49 

0.6729 

0.1086 

94 

0.6912 

0.2174 

139 

0  .  7270 

0.3469 

5 

0.6667 

0.0109 

50 

0.6732 

0.1109 

95 

0.6918 

0.2200 

140 

0.7281 

0.3501 

6 

0.6667 

0.0131 

51 

0.6734 

0.1131 

96 

0.6924 

0  .  2226 

141 

0  .  7292 

0.3534 

7 

0.6668 

0.0153 

52 

0  .  6737 

0.1154 

97 

0.6930 

0.2252 

142 

0  .  7303 

0.3567 

8 

0.6668 

0.0175 

53 

0.6740 

0.1177 

98 

0.6936 

0.2279 

143 

0.7314 

0.3600 

9 

0.6669 

0.0197 

54 

0.6743 

0  .  1200 

99 

0.6942 

0.2305 

144 

0.7325 

0.3633 

10 

0.6670 

0.0218 

55 

0.6746 

0  .  1224 

100 

0.6948 

0.2332 

145 

0.7336 

0.3666 

11 

0  .  6670 

0.0240 

56 

0.6749 

0.1247 

101 

0.6954 

0.2358 

146 

0.7348 

0.3700 

12 

0.6671 

0  .  0262 

57 

0.6752 

0.1270 

102 

0.6961 

0.2385 

147 

0.7360 

0  .  3734 

13 

0.6672 

0  .  0284 

58 

0.6755 

0.1293 

103 

0.6967 

0.2412 

148 

0.7372 

0  .  3768 

14 

0.6672 

0  .  0306 

59 

0.6758 

0.1316 

104 

0.6974 

0.2439 

149 

0.7384 

0.3802 

15 

0.6673 

0.0328 

60 

0.6761 

0  .  1340 

105 

0  .  6980 

0.2466 

150 

0  .  7396 

0.3837 

16 

0  .  6674 

0.0350 

61 

0.6764 

0.1363 

106 

0.6987 

0.2493 

151 

0.7408 

0.3872 

17 

0.6674 

0.0372 

62 

0.6768 

0  .  1387 

107 

0  .  6994 

0.2520 

152 

0.7421 

0.3901 

18 

0.6675 

0  .  0394 

63 

0.6771 

0.1410 

108 

0.7001 

0.2548 

153 

0  .  7434 

0.3946 

19 

0.6676 

0.0416 

64 

0.6775 

0  .  1434 

109 

0.7008 

0.2575 

154 

0.7447 

0.3977 

20 

0.6677 

0  .  0437 

65 

0  .  6779 

0.1457 

110 

0.7015 

0.2603 

155 

0.7460 

0.4013 

21 

0.6678 

0  .  0459 

66 

0.6782 

0  .  1481 

111 

0.7022 

0.2631 

156 

0.7473 

0.4049 

22 

0  .  6679 

0  .  0481 

67 

0.6786 

0.1505 

112 

0.7030 

0.2659 

157 

0.7486 

0.4085 

23 

0.6680 

0.0504 

68 

0.6790 

0.1529 

113 

0  .  7037 

0.2687 

158 

0.7500 

0.4122 

24 

0.6681 

0.0526 

69 

0.6794 

0.1553 

114 

0.7045 

0.2715 

159 

0.7514 

0.4159 

25 

0.6682 

0.0548 

70 

0.6797 

0.1577 

115 

0.7052 

0.2743 

160 

0.7528 

0.4196 

26 

0.6684 

0.0570 

71 

0.6801 

0.1601 

116 

0.7060 

0.2772 

161 

0.7542 

0  .  4233 

27 

0.6685 

0.0592 

72 

0.6805 

0.1625 

117 

0.7068 

0.2800 

162 

0.7557 

0.4270 

28 

0.6687 

0.0614 

73 

0.6809 

0.1649 

118 

0.7076 

0.2829 

163 

0.7571 

0.4308 

29 

0.6688 

0.0636 

74 

0.6814 

0.1673 

119 

0.7084 

0.2858 

164 

0.7586 

0.4346 

30 

0.6690 

0.0658 

75 

0.6818 

0.1697 

120 

0.7092 

0.2887 

165 

0.7601 

0.4385 

31 

0.6691 

0.0681 

76 

0  .  6822 

0.1722 

121 

0.7100 

0.2916 

166 

0.7616 

0  .  4424 

32 

0.6693 

0.0703 

77 

0.6826 

0.1746 

122 

0.7109 

0.2945 

167 

0.7632 

0.4463 

33 

0.6694 

0.0725 

78 

0.6831 

0.1771 

123 

0.7117 

0.2975 

168 

0.7648 

0.4502 

34 

0.6696 

0.0747 

79 

0.6835 

0.1795 

124 

0.7126 

0.3004 

169 

0.7664 

0.4542 

35 

0.6698 

0.0770 

80 

0  .  6840 

0.1820 

125 

0.7134 

0.3034 

170 

0.7680 

0.4582 

36 

0.6700 

0.0792 

81 

0.6844 

0.1845 

126 

0.7143 

0.3064 

171 

0.7696 

0.4622 

37 

0  .  6702 

0.0814 

82 

0  .  6849 

0  .  1869 

127 

0.7152 

0.3094 

172 

0.7712 

0.4663 

38 

0.6704 

0  .  0837 

83 

0.6854 

0.1894 

128 

0.7161 

0.3124 

173 

0.7729 

0.4704 

39 

0.6706 

0.0859 

84 

0.6859 

0.1919 

129 

0.7170 

0.3155 

174 

0.7746 

0.4745 

40 

0.6708 

0.0882 

85 

0.6864 

0  .  1944 

130 

0.7180 

0.3185 

175 

0.7763 

0.4787 

41 

0.6710 

0.0904 

86 

0.6869 

0.1970 

131 

0.7189 

0.3216 

176 

0.7781 

0.4828 

42 

0.6712 

0  .  0927 

87 

0.6874 

0.1995 

132 

0.7199 

0.3247 

177 

0.7799 

0.4871 

43 

0.6714 

0.0949 

88 

0.6879 

0  .  2020 

133 

0.7209 

0.3278 

178 

0.7817 

0.4914 

44 

0.6717 

0.0972 

89 

0.6884 

0.2046 

134 

0.7219, 

0  .  3309 

179 

0.7835 

0.4957 

45 

0.6719 

0.0995 

90 

0  6890 

0.2071 

135 

0.7229 

0.3341 

180 

0.7854 

0.5000 

174 


USEFUL      DATA 


2  i 


i 

Si 
I 

'a 


& 


O2 


«    C 


cq 


1 


e|-o   e    o 


1    -1 


«        e 


175 


CORRUGATED   BAR   COMPANY,  INC. 


NATURAL  TRIGONOMETRIC   FUNCTIONS 


SINES 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

0 

0.00000 

0.00291 

0.00582 

0.00873 

0.01164 

0.01454 

0.01745 

89 

1 

0.01745 

0.02036 

0.02327 

0.02618 

0.02908 

0.03199 

0.03490 

88 

2 

0.03490 

0.03781 

0.04071 

0.04362 

0.04653 

0.04943 

0.05234 

87 

3 

0.05234 

0.05524 

0.05814 

0.06105 

0.06395 

0.06685 

0.06976 

86 

4 

0.06976 

0.07266 

0.07556 

0.07846 

0.08136 

0.08426 

0.08716 

85 

5 

0.08716 

0.09005 

0.09295 

0.09585 

0.09874 

0.10164 

0.10453 

84 

6 

0.10453 

0.10742 

0.11031 

0.11320 

0.11609 

0.11898 

0.12187 

83 

7 

0.12187 

0.12476 

0.12764 

0.13053 

0.13341 

0.13629 

0.13917 

82 

8 

0.13917 

0.14205 

0.14493 

0.14781 

0.15069 

0.15356 

0.15643 

81 

9 

0.15643 

0.15931 

0.16218 

0.16505 

0.16792 

0.17078 

0.17365 

80 

10 

0.17365 

0.17651 

0.17937 

0.18224 

0.18509 

0.18795 

0.19081 

79 

11 

0.19081 

0.19366 

0.19652 

0.19937 

0.20222 

0.20507 

0.20791 

78 

12 

0.20791 

0.21076 

0.21360 

0.21644 

0.21928 

0.22212 

0.22495 

77 

13 

0.22495 

0.22778 

0.23062 

0.23345 

0.23627 

0.23910 

0.24192 

76 

14 

0.24192 

0.24474 

0.24756 

0.25038 

0.25320 

0.25601 

0.25882 

75 

15 

0.25882 

0.26163 

0.26443 

0.26724 

0.27004 

0.27284 

0.27564 

74 

16 

0.27564 

0.27843 

0.28123 

0.28402 

0.28680 

0.28959 

0.29237 

73 

17 

0.29237 

0.29515 

0.29793 

0.30071 

0.30348 

0.30625 

0.30902 

72 

18 

0.30902 

0.31178 

0.31454 

0.31730 

0.32006 

0.32282 

0.32557 

71 

19 

0.32557 

0.32832 

0.33106 

0.33381 

0.33655 

0.33929 

0.34202 

70 

20 

0.34202 

0.34475 

0.34748 

0.35021 

0.35293 

0.35565 

0.35837 

69 

21 

0.35837 

0.36108 

0.36379 

0.36650 

0.36921 

0.37191 

0.37461 

68 

22 

0.37461 

0.37730 

0.37999 

0.38268 

0.38537 

0.38805 

0.39073 

67 

23 

0.39073 

0.39341 

0.39608 

0.39875 

0.40142 

0.40408 

0.40674 

66 

24 

0.40674 

0.40939 

0.41204 

0.41469 

0.41734 

0.41998 

0.42262 

65 

25 

0.42262 

0.42525 

0.42788 

0.43051 

0.43313 

0.43575 

0.43837 

64 

26 

0.43837 

0.44098 

0.44359 

0.44620 

0.44880 

0.45140 

0.45399 

63 

27 

0.45399 

0.45658 

0.45917 

0.46175 

0.46433 

0.46690 

0.46947 

62 

28 

0.46947 

0.47204 

0.47460 

0.47716 

0.47971 

0.48226 

0.48481 

61 

29 

0.48481 

0.48735 

0.48989 

0.49242 

0.49495 

0.49748 

0.50000 

60 

30 

0.50000 

0.50252 

0.50503 

0.50754 

0.51004 

0.51254 

0.51504 

59 

31 

0.51504 

0.51753 

0.52002 

0.52250 

0.52498 

0.52745 

0.52992 

58 

32 

0.52992 

0.53238 

0.53484 

0.53730 

0.53975 

0.54220 

0.54464 

57 

33 

0.54464 

0.54708 

0.54951 

0.55194 

0.55436 

0.55678 

0.55919 

56 

34 

0.55919 

0.56160 

0.56401 

0.56641 

0.56880 

0.57119 

0.57358 

55 

35 

0.57358 

0.57596 

0.57833 

0.58070 

0.58307 

0.58543 

0.58779 

54 

36 

0.58779 

0.59014 

0.59248 

0.59482 

0.59716 

0.59949 

0.60182 

53 

37 

0.60182 

0.60414 

0.60645 

0.60876 

0.61107 

0.61337 

0.61566 

52 

38 

0.61566 

0.61795 

0.62024 

0.62251 

0.62479 

0.62706 

0.62932 

51 

39 

0.62932 

0.63158 

0.63383 

0.63608 

0.63832 

0.64056 

0.64279 

50 

40 

0.64279 

0.64501 

0.64723 

0.64945 

0.65166 

0.65386 

0.65606 

49 

41 

0.65606 

0.65825 

0.66044 

0.66262 

0.66480 

0.66697 

0.66913 

48 

42 

0.66913 

0.67129 

0.67344 

0.67559 

0.67773 

0.67987 

0.68200 

47 

43 

0.68200 

0.68412 

0.68624 

0.68835 

0.69046 

0.69256 

0.69466 

46 

44 

0.69466 

0.69675 

0.69883 

0.70091 

0.70298 

0.70505 

0.70711 

45 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

COSINES 


176 


USEFUL      DATA 


NATURAL  TRIGONOMETRIC   FUNCTIONS 


COSINES 


0' 

10'       20'       30'       40'       50'    |    60' 

0 

1.00000 

1.00000 

0.99998 

0.99996 

0.99993 

0.99989 

0.99985 

89 

1 

0.99985 

0.99979 

0.99973 

0.99966 

0.99958 

0.99949 

0.99939 

88 

2 

0.99939 

0.99929 

0.99917 

0.99905 

0.99892 

0.99878 

0.99863 

87 

3 

0.99863 

0.99847 

0.99831 

0.99813 

0.99795 

0.99776 

0.99756 

86 

4 

0.99756 

0.99736 

0.99714 

0.99692 

0.99668 

0.99644 

0.99619 

85 

5 

0.99619 

0.99594 

0.99567 

0.99540 

0.99511 

0.99482 

0.99452 

84 

6 

0.99452 

0.99421 

0.99390 

0.99357 

0.99324 

0.99290 

0.99255 

83 

7 

0.99255 

0.99219 

0.99182 

0.99144 

0.99106 

0.99067 

0.99027 

82 

8 

0.99027 

0.98986 

0.98944 

0.98902 

0.98858 

0.98814 

0.98769 

81 

9 

0.98769 

0.98723 

0.98676 

0.98629 

0.98580 

0.98531 

0.98481 

80 

10 

0.98481 

0.98430 

0.98378 

0.98325 

0.98272 

0.98218 

0.98163 

79 

11 

0.98163 

0.98107 

0.98050 

0.97992 

0.97934 

0.97875 

0.97815 

78 

12 

0.97815 

0.97754 

0.97692 

0.97630 

0.97566 

0.97502 

0.97437 

77 

13 

0.97437 

0.97371 

0.97304 

0.97237 

0.97169 

0.97100 

0.97030 

76 

14 

0.97030 

0.96959 

0.96887 

0.96815 

0.96742 

0.96667 

0.96593 

75 

15 

0.96593 

0.96517 

0.96440 

0.96363 

0.96285 

0.96206 

0.96126 

74 

16 

0.96126 

0.96046 

0.95964 

0.95882 

0.95799 

0.95715 

0.95630 

73 

17 

0.95630 

0.95545 

0.95459 

0.95372 

0.95284 

0.95195 

0.95106 

72 

18 

0.95106 

0.95015 

0.94924 

0.94832 

0.94740 

0.94646 

0.94552 

71 

19 

0.94552 

0.94457 

0.94361 

0.94264 

0.94167 

0.94068 

0.93969 

70 

20 

0.93969 

0.93869 

0.93769 

0.93667 

0.93565 

0.93462 

0.93358 

69 

21 

0.93358 

0.93253 

0.93148 

0.93042 

0.92935 

0.92827 

0.92718 

68 

22 

0.92718 

0.92609 

0.92499 

0.92388 

0.92276 

0.92164 

0.92050 

67 

23 

0.92050 

0.91936 

0.91822 

0.91706 

0.91590 

0.91472 

0.91355 

66 

24 

0.91355 

0.91236 

0.91116 

0.90996 

0.90875 

0.90753 

0.90631 

65 

25 

0.90631 

0.90507 

0.90383 

0.90259 

0.90133 

0.90007 

0.89879 

64 

26 

0.89879 

0.89752 

0.89623 

0.89493 

0.89363 

0.89232 

0.89101 

63 

27 

0.89101 

0.88968 

0.88835 

0.88701 

0.88566 

0.88431 

0.88295 

62 

28 

0.88295 

0.88158 

0.88020 

0.87882 

0.87743 

0.87603 

0.87462 

61 

29 

0.87462 

0.87321 

0.87178 

0.87036 

0.86892 

0.86748 

0.86603 

60 

30 

0.86603 

0.86457 

0.86310 

0.86163 

0.86015 

0.85866 

0.85717 

59 

31 

0.85717 

0.85567 

0.85416 

0.85264 

0.85112 

0.84959 

0.84805 

58 

32 

0.84805 

0.84650 

0.84495 

0.84339 

0.84182 

0.84025 

0.83867 

57 

33 

0.83867 

0.83708 

0.83549 

0.83389 

0.83228 

0.83066 

0.82904 

56 

34 

0,82904 

0.82741 

0.82577 

0.82413 

0.82248 

0.82082 

0.81915 

55 

35 

0.81915 

0.81748 

0.81580 

0.81412 

0.81242 

0.81072 

0.80902 

54 

36 

0.80902 

0.80730 

0.80558 

0.80386 

0.80212 

0.80038 

0.79864 

53 

37 

0.79864 

0.79688 

0.79512 

0.79335 

0.79158 

0.78980 

0.78801 

52 

38 

0.78801 

0.78622 

0.78442 

0.78261 

0.78079 

0.77897 

0.77715 

51 

39 

0.77715 

0.77531 

0.77347 

0.77162 

0.76977 

0.76791 

0.76604 

50 

40 

0.76604 

0.76417 

0.76229 

0.76041 

0.75851 

0.75661 

0.75471 

49 

41 

0.75471 

0.75280 

0.75088 

0.74896 

0.74703 

0.74509 

0.74314 

48 

42 

0.74314 

0.74120 

0.73924 

0.73728 

0.73531 

0.73333 

0.73135 

47 

43 

0.73135 

0.72937 

0.72737 

0.72537 

0.72337 

0.72136 

0.71934 

46 

44 

0.71934 

0.71732 

0.71529 

0.71325 

0.71121 

0.70916 

0.70711 

45 

60' 

50' 

40' 

30' 

20'       10' 

0' 

SINES 


177 


CORRUGATED   BAR   COMPANY,  INC. 


NATURAL  TRIGONOMETRIC  FUNCTIONS 


J.  AJNliHiNia 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

0 

0.00000 

0.00291 

0.00582 

0.00873 

0.01164 

0.01455 

0.01746 

89 

1 

0.01746 

0.02036 

0.02328 

0.02619 

0.02910 

0.03201 

0.03492 

88 

2 

0.03492 

0.03783 

0.04075 

0.04366 

0.04658 

0.04949 

0.05241 

87 

3 

0.05241 

0.05533 

0.05824 

0.06116 

0.06408 

0.06700 

0.06993 

86 

4 

0.06993 

0.07285 

0.07578 

0.07870 

0.08163 

0.08456 

0.08749 

85 

5 

0.08749 

0.09042 

0.09335 

0.09629 

0.09923 

0.10216 

0.10510 

84 

6 

0.10510 

0.10805 

0.11099 

0.11394 

0.11688 

0.11983 

0.12278 

83 

7 

0.12278 

0.12574 

0.12869 

0.13165 

0.13461 

0.13758 

0.14054 

82 

8 

0.14054 

0.14351 

0.14648 

0.14945 

0.15243 

0.15540 

0.15838 

81 

9 

0.15838 

0.16137 

0.16435 

0.16734 

0.17033 

0.17333 

0.17633 

80 

10 

0.17633 

0.17933 

0.18233 

0.18534 

0.18835 

0.19136 

0.19438 

79 

11 

0.19438 

0.19740 

0.20042 

0.20345 

0.20648 

0.20952 

0.21256 

78 

12 

0.21256 

0.21560 

0.21864 

0.22169 

0.22475 

0.22781 

0.23087 

77 

13 

0.23087 

0.23393 

0.23700 

0.24008 

0.24316 

0.24624 

0.24933 

76 

14 

0.24933 

0.25242 

0.25552 

0.25862 

0.26172 

0.26483 

0.26795 

75 

15 

0.26795 

0.27107 

0.27419 

0.27732 

0.28046 

0.28360 

0.28675 

74 

16 

0.28675 

0.28990 

0.29315 

0.29621 

0.29938 

0.30255 

0.30573 

73 

17 

0.30573 

0.30891 

0.31210 

0.31530 

0.31850 

0.32171 

0.32492 

72 

18 

0.32492 

0.32814 

0.33136 

0.33460 

0.33783 

0.34108 

0.34433 

71 

19 

0.34433 

0.34758 

0.35085 

0.35412 

0.35740 

0.36068 

0.36397 

70 

20 

0.36397 

0.36727 

0.37057 

0.37388 

0.37720 

0.38053 

0.38386 

69 

21 

0.38386 

0.38721 

0.39055 

0.39391 

0.39727 

0.40065 

0.40403 

68 

22 

0.40403 

0.40741 

0.41081 

0.41421 

0.41763 

0.42105 

0.42447 

67 

23 

0.42447 

0.42791 

0.43136 

0.43481 

0.43828 

0.44175 

0.44523 

66 

24 

0.44523 

0.44872 

0.45222 

0.45573 

0.45924 

0.46277 

0.46631 

65 

25 

0.46631 

0.46985 

0.47341 

0.47698 

0.48055 

0.48414 

0.48773 

64 

26 

0.48773 

0.49134 

0.49495 

0.49858 

0.50222 

0.50587 

0.50953 

63 

27 

0.50953 

0.51320 

0.51688 

0.52057 

0.52427 

0.52798 

0.53171 

62 

28 

0.53171 

0.53545 

0.53920 

0.54296 

0.54674 

0.55051 

0.55431 

61 

29 

0.55431 

0.55812 

0.56194 

0.56577 

0.56962 

0.57348 

0.57735 

60 

30 

0.57735 

0.58124 

0.58513 

0.58905 

0.59297 

0.59691 

0.60086 

59 

31 

0.60086 

0.60483 

0.60881 

0.61280 

0.61681 

0.62083 

0.62487 

58 

32 

0.62487 

0.62892 

0.63299 

0.63707 

0.64117 

0.64528 

0.64941 

57 

33 

0.64941 

0.65355 

0.65771 

0.66189 

0.66608 

0.67028 

0.67451 

56 

34 

0.67451 

0.67875 

0.68301 

0.68728 

0.69157 

0.69588 

0.70021 

55 

35 

0.70021 

0.70455 

0.70891 

0.71329 

0.71769 

0.72211 

0.72654 

54 

36 

0.72654 

0.73100 

0.73547 

0.73996 

0.74447 

0.74900 

0.75355 

53 

37 

0.75355 

0.75812 

0.76272 

0.76733 

0.77196 

0.77661 

0.78129 

52 

38 

0.78129 

0.78598 

0.79070 

0.79544 

0.80020 

0.80498 

0.80978 

51 

39 

0.80978 

0.81461 

0.81946 

0.82434 

0.82923 

0.83415 

0.83910 

50 

40 

0.83910 

0.84407 

0.84906 

0.85408 

0.85912 

0.86419 

0.86929 

49 

41 

0.86929 

0.87441 

0.87955 

0.88473 

0.88992 

0.89515 

0.90040 

48 

42 

0.90040 

0.90569 

0.91099 

0.91633 

0.92170 

0.92709 

0.93252 

47 

43 

0.93252 

0.93797 

0.94345 

0.94896 

0.95451 

0.96008 

0.96569 

46 

44 

0.96569 

0.97133 

0.97700 

0.98270 

0.98843 

0.99420 

1.00000 

45 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

COTANGENTS 


178 


USEFUL      DATA 


NATURAL  TRIGONOMETRIC  FUNCTIONS 


C 

OTANGENTS 

0' 

107 

20' 

30' 

40' 

50' 

60' 

0 

00 

343.77371 

171.88540 

114.58865 

85.93979 

68.75009 

57.28996 

89 

1 

57.28996 

49.10388 

42.96408 

38.18846 

34.36777 

31.24158 

28.63625 

88 

2 

28.63625 

26.43160 

24.54176 

22.90377 

21.47040 

20.20555 

19.08114 

87 

3 

19.08114 

18.07498 

17.16934 

16.34986 

15.60478 

14.92442 

14.30067 

86 

4 

14.30067 

14.72674 

13.19688 

12.70621 

12.25051 

11.82617 

11.43005 

85 

5 

11.43005 

11.05943 

10.71191 

10.38540 

10.07803 

9.78817 

9.51436 

84 

6 

9.51436 

9.25530 

9.00983 

8.77689 

8.55555 

8.34496 

8.14435 

83 

7 

8.14435 

7.95302 

7.77035 

7.59575 

7.42871 

7.26873 

7.11537 

82 

8 

7.11537 

6.96823 

6.82694 

6.69116 

6.56055 

6.43484 

6.31375 

81 

9 

6.31375 

6.19703 

6.08444 

5.97576 

5.87080 

5.76937 

5.67128 

80 

10 

5.67128 

5.57638 

5.48451 

5.39552 

5.30928 

5.22566 

5.14455 

79 

11 

5.14455 

5.06584 

4.98940 

4.91516 

4.84300 

4.77286 

4.70463 

78 

12 

4.70463 

4.63825 

4.57363 

4.51071 

4.44942 

3.38969 

4.33148 

77 

13 

4.33148 

4.27471 

4.21933 

4.16530 

4.11256 

4.06107 

4.01078 

76 

14 

4.01078 

3.96165 

3.91364 

3.86671 

3.82083 

3.77595 

3.73205 

75 

15 

3.73205 

3.68900 

3.64705 

3.60588 

3.56557 

3.52609 

3.48741 

74 

16 

3.48741 

3.44951 

3.41236 

3.37594 

3.34023 

3.30521 

3.27085 

73 

17 

3.27085 

3.23714 

3.20406 

3.17159 

3.13972 

3.10842 

3.07778 

72 

18 

3.07768 

3.04749 

3.01783 

2.98869 

2.96004 

2.93189 

2.90421 

71 

19 

2.90421 

2.87700 

2.85023 

2.82391 

2.79802 

2.77254 

2.74748 

70 

20 

2.74748 

2.72281 

2.69853 

2.67462 

2.65109 

2.62791 

2.60509 

69 

21 

2.60509 

2.58261 

2.56046 

2.53865 

2.51715 

2.49597 

2.47509 

68 

22 

2.47509 

2.45451 

2.43422 

2.41421 

2.39449 

2.37504 

2.35585 

67 

23 

2.35585 

2.33693 

2.31826 

2.29984 

2.28167 

2.26374 

2.24604 

66 

24 

2.24604 

2.22857 

2.21132 

2.19430 

2.17749 

2.16090 

2.14451 

65 

25 

2.14451 

2.12832 

2.11233 

2.09654 

2.08094 

2.06553 

2:05030 

64 

26 

2.05030 

2.03526 

2.02039 

2.00569 

.99116 

.97680 

.96261 

63 

27 

1.96261 

.94858 

1.93470 

1.92098 

.90741 

.89400 

.88073 

62 

28 

1.88073 

.86760 

1.85462 

1.84177 

.§2907 

.81649 

.80405 

61 

29 

1.80405 

.79174 

1.77955 

1.76749 

.75556 

.74375 

.73205 

60 

30 

1.73205 

.72047 

1.70901 

1.69766 

.68643 

.67530 

.66428 

59 

31 

1.66428 

.65337 

1.64256 

1.63185 

.62125 

.61074 

.60033 

58 

32 

1.60033 

.59002 

1.57981 

1.56969 

.55966 

.54972 

1.53987 

57 

33 

1.53987 

1.53010 

1.52043 

1.51084 

.50133 

.49190 

1.48256 

56 

34 

1.48250 

1.47330 

1.46411 

1.45501 

.44598 

1.43703 

1.42815 

55 

35 

1.42815 

1.41934 

1.41061 

1.40195 

.39336 

1.38484 

1.37638 

54 

36 

1.37638 

1.36800 

1.35968 

1.35142 

.34323 

1.33511 

1.32704 

53 

37 

1.32704 

1.31904 

1.31110 

1.30323 

.29541 

1.28764 

1.27994 

52 

38 

1.27994 

1.27230 

1.26471 

1.25717 

.24969 

.24227 

1.23490 

51 

39 

1.23490 

1.22758 

1.22031 

1.21310 

.20593 

.19882 

1.19175 

50 

40 

1.19175 

1.18474 

1  .  17777 

1.17085 

.  16398 

.15715 

1  .  15037 

49 

41 

1.15037 

1.14363 

1  .  13694 

1.13029 

.  12369 

.11713 

1.11061 

48 

42 

1.11061 

1  .  10414 

1.09770 

1.09131 

.08496 

.07864 

1.07237 

47 

43 

1.07237 

1.06613 

1.05994 

1.05378 

1.04766 

.04158 

1.03553 

46 

44 

1.03553 

1.02952 

1.02355 

1.01761 

.01170 

.00583 

1.00000 

45 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

TANGENTS 


179 


CORRUGATED      BAR      COMPANY,     INC. 


NATURAL  TRIGONOMETRIC  FUNCTIONS 


SECANTS 

0' 

10' 

20' 

30'    | 

40' 

50' 

60' 

0 

1.00000 

.00000 

1.00002 

.00004 

1.00007 

1.00011 

1.00015 

89 

1 

1.00015 

.00021 

.00027 

.00034 

1.00042 

1.00051 

1.00061 

88 

2 

1.00061 

.00072 

.00083 

.00095 

1.00108 

1.00122 

1.00137 

87 

3 

1.00137 

.00153 

.00169 

.00187 

1.00205 

1.00224 

1.00244 

86 

4 

1.00244 

.00265 

.00287 

.00309 

1.00333 

1.00357 

1.00382 

85 

5 

1.00382 

.00408 

.00435 

.00463 

1.00491 

1.00521 

1.00551 

84 

6 

1.00551 

.00582 

.00614 

.00647 

1.00681 

1.00715 

1.00751 

83 

7 

1.00751 

.00787 

.00825 

.00863 

1.00902 

1.00942 

1.00983 

82 

8 

1.00983 

.01024 

.01067 

.01111 

1.01155 

1.01200 

1.01247 

81 

9 

1.01247 

.01294 

.01342 

.01391 

1.01440 

1.01491 

1.01543 

80 

10 

1.01543 

.01595 

.01649 

.01703 

1.01758 

1.01815 

1.01872 

79 

11 

1.01872 

.01930 

.01989 

.02049 

1.02110 

1.02171 

1.02234 

78 

12 

1.02234 

.02298 

.02362 

.02428 

1.02494 

1.02562 

1.02630 

77 

13 

1.02630 

1.02700 

.02770 

.02842 

1.02914 

1.02987 

1.03061 

76 

14 

1.03061 

1.03137 

.03213 

.03290 

1.03368 

1.03447 

1.03528 

75 

15 

1.03528 

1.03609 

1.03691 

.03774 

1.03858 

1.03944 

1.04030 

74 

16 

1.04030 

.04117 

1.04206 

.04295 

1.04385 

1.04477 

1.04569 

73 

17 

1.04569 

.04663 

1.04757 

.04853 

1.04950 

1.05047 

1.05146 

72 

18 

1.05146 

.05246 

.05347 

.05449 

1.05552 

1.05657 

.05762 

71 

19 

1.05762 

.05869 

.05976 

.06085 

1.06195 

1.06306 

.06418 

70 

20 

1.06418 

.06531 

.06645 

1.06761 

1.06878 

1.06995 

.07115 

69 

21 

1.07115 

.07235 

.07356 

1.07479 

1.07602 

1.07727 

.07853 

68 

22 

1.07853 

.07981 

.08109 

1.08239 

1.08370 

1.08503 

.08636 

67 

23 

1.08636 

.08771 

.08907 

1.09044 

1.09183 

1.09323 

.09464 

66 

24 

1.09464 

.09605 

.09750 

1.09895 

1  .  10041 

1  .  10189 

.10338 

65 

25 

1.10338 

1.10488 

.10640 

1.10793 

1.10947 

1.11103 

.11260 

64 

26 

1.11260 

1.11419 

.11579 

1.11740 

1.11903 

1.12067 

.12233 

63 

27 

1.12233 

1  .  12400 

.12568 

1.12738 

1.12910 

1.13083 

.13257 

62 

28 

1.13257 

1  .  13433 

43610 

1.13789 

1  .  13970 

1.14152 

.  14335 

61 

29 

1.14335 

1  .  14521 

.  14707 

1.14896 

1.15085 

1  .  15277 

.15470 

60 

30 

1  .  15470 

1.15665 

.  15861 

1  .  16059 

1  .  16259 

1.16460 

.16663 

59 

31 

1.16663 

1.16868 

.17075 

1.17283 

1  .  17493 

1.17704 

.17918 

58 

32 

1.17918 

1  .  18133 

.18350 

1  .  18569 

1.18790 

1.19012 

.  19236 

57 

33 

1  .  19236 

1  .  19463 

.19691 

1.19920 

1.20152 

1.20386 

.20622 

56 

34 

1.20622 

1.20859 

.21099 

1.21341 

1.21584 

1.21830 

.22077 

55 

35 

1.22077 

.22327 

.22579 

1.22833 

1.23089 

1.23347 

.23607 

54 

36 

1.23607 

.23869 

.24134 

1.24400 

1.24669 

1.24940 

.25214 

53 

37 

1.25214 

.25489 

.25767 

1.26047 

1.26330 

1.26615 

.26902 

52 

38 

1.26902 

.27191 

.27483 

1.27778 

1.28075 

1.28374 

.28676 

51 

39 

1.28676 

.28980 

.29287 

1.29597 

1.29909 

1.30223 

.30541 

50 

40 

1.30541 

.30861 

1.31183 

1.31509 

1.31837 

1.32168 

.32501 

49 

41 

1.32501 

.32838 

1.33177 

1.33519 

1.33864 

1.34212 

.34563 

48 

42 

1.34563 

.34917 

1.35274 

1.35634 

1.35997 

1.36363 

1.36733 

47 

43 

1.36733 

.37105 

1.37481 

1.37860 

1.38242 

1.38628 

1.39016 

46 

44 

1.39016 

.39409 

1.39804 

1.40203 

1.40606 

1.41012 

1.41421 

45 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

COSECANTS 


180 


USEFUL      DATA 


NATURAL  TRIGONOMETRIC   FUNCTIONS 


COSECANTS 

0' 

10 

20' 

30' 

40' 

50' 

60' 

0 

X 

343.77516 

171.88831 

114.59301 

85.94561 

68.75736 

57.29869 

89 

1 

57.29869 

49.11406 

42.97571 

38.20155 

34.38232 

31.25758 

28.65371 

88 

2 

28.65371 

26.45051 

24.56212 

22.92559 

21.49368 

20.23028 

19.10732 

87 

3 

19.10732 

18.10262 

17.19843 

16.38041 

15.63679 

14.95788 

14.33559 

86 

4 

14.33559 

13.76312 

13.23472 

12.74550 

12.29125 

11.86837 

11.47371 

85 

5 

11.47371 

11.10455 

10.75849 

10.43343 

10.12752 

9.83912 

9.56677 

84 

6 

9.56677 

9.30917 

9.06515 

8.83367 

8.61379 

8.40466 

8.20551 

83 

7 

8.20551 

8.01565 

7.83443 

7.66130 

7.49571 

7.33719 

7.18530 

82 

8 

7.18530 

7.03962 

6.89979 

6.76547 

6.63633 

6.51208 

6.39245 

81 

9 

6.39245 

6.27719 

6.16607 

6.05886 

5.95536 

5.85539 

5.75877 

80 

10 

5.75877 

5.66533 

5.57493 

5.48740 

5.40263 

5.32049 

5.24084 

79 

11 

5.24084 

5.16359 

5.08863 

5.01585 

4.94517 

4.87649 

4.80973 

78 

12 

4.80973 

4.74482 

4.68167 

4.62023 

4.56041 

4.50216 

4.44541 

77 

13 

4.44541 

4.39012 

4.33622 

4.28366 

4.23239 

4.18238 

4.13357 

76 

14 

4.13357 

4.08591 

4.03938 

3.99393 

3.94952 

3.90613 

3.86370 

75 

15 

3.86370 

3.82223 

3.78166 

3.74198 

3.70315 

3.66515 

3.62796 

74 

16 

3.62796 

3.59154 

3.55587 

3.52094 

3.48671 

3.45317 

3.42030 

73 

17 

3.42030 

3.38808 

3.35649 

3.32551 

3.29512 

3.26531 

3.23607 

72 

18 

3.23607 

3.20737 

3.17920 

3.15155 

3.12440 

3.09774 

3.07155 

71 

19 

3.07155 

3.04584 

3.02057 

2.99574 

2.97135 

2.94737 

2.92380 

70 

20 

2.92380 

2.90063 

2.87785 

2.85545 

2.83342 

2.81175 

2.79043 

69 

21 

2.79043 

2.76945 

2.74881 

2.72850 

2.70851 

2.68884 

2.66947 

68 

22 

2.66947 

2.65040 

2.63162 

2.61313 

2.59491 

2.57698 

2.55930 

67 

23 

2.55930 

2.54190 

2.52474 

2.50784 

2.49119 

2.47477 

2.45959 

66 

24 

2.45859 

2.44264 

2.42692 

2.41142 

2.39614 

2.38107 

2.36620 

65 

25 

2.36620 

2.35154 

2.33708 

2.32282 

2.30875 

2.29487 

2.28117 

64 

26 

2.28117 

2.26766 

2.25432 

2.24116 

2.22817 

2.21535 

2.20269 

63 

27 

2.20269 

2.19019 

2.17786 

2.16568 

2.15366 

2.14178 

2.13005 

62 

28 

2.13005 

2.11847 

2.10704 

2.09574 

2.08458 

2.07356 

2.06267 

61 

29 

2.06267 

2.05191 

2.04128 

2.03077 

2.02039 

2.01014 

2.00000 

60 

30 

2.00000 

1.98998 

1.98008 

1.97029 

.96062 

1.95106 

1.94160 

59 

31 

.94160 

1.93226 

1.92302 

1.91388 

.90485 

1.89591 

.88709 

58 

32 

.88708 

1.87834 

1.86970 

1.86116 

.85271 

1.84435 

.83608 

57 

33 

.83608 

1.82790 

1.81981 

1.81180 

.80388 

1.79604 

.78829 

56 

34 

.78829 

1.78062 

1.77303 

1.76552 

.75808 

1.75073 

.74345 

55 

35 

.74345 

1.73624 

1.72911 

1.72205 

.71506 

1.70815 

.70130 

54 

36 

.70130 

1.69454 

1.68782 

1.68117 

.67460 

1.66809 

.66164 

53 

37 

.66164 

1.65526 

1.64894 

1.64268 

.63648 

1.63035 

.62427 

52 

38 

.62427 

1.61825 

1.61229 

1.60639 

.60054 

.59475 

.58902 

51 

39 

.58902 

1.58333 

1.57771 

1.57213 

.56661 

.56114 

.55572 

50 

40 

1.55572 

1.55036 

1.54504 

1.53977 

1.53455 

.52938 

.52425 

49 

41 

1.52425 

1.51918 

1.51415 

1.50916 

1.50422 

.49933 

.49448 

48 

42 

1.49448 

1.48967 

1.48491 

1.48019 

1.47551 

.47087 

.46628 

47 

43 

1.46628 

1.46173 

1.45721 

1.45274 

1.44831 

.44391 

.43856 

46 

44 

1.43956 

1.43524 

1.43096 

1.42672 

1.42251 

.41835 

.41421 

45 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

SECANTS 


181 


CORRUGATED      BAR      COMPANY,     INC. 


FUNCTIONS  OF  NUMBERS   1  TO  49 


XTrt 

xi,,i_  - 

Square 

Cube 

1,000 
x 

No.  =  E 

HAMETER 

.NO. 

Square 

Cube 

Root 

Root 

Logarithm 

Reciprocal 

Circum. 

Area 

l 

1 

i 

1.0000 

1.0000 

0.00000 

1000.000 

3.142 

0/7854 

2 

4 

8 

1.4142 

1.2599 

0.30103 

500.000 

6.283 

3.1416 

3 

9 

27 

1.7321 

1.4422 

0.47712 

333.333 

9.425 

7.0686 

4 

16 

64 

2.0000 

1.5874 

0.60206 

250.000 

12.566 

12.5664 

5 

25 

125 

2.2361 

1.7100 

0.69897 

200.000 

15.708 

19.6350 

6 

36 

216 

2.4495 

1.8171 

0.77815 

166.667 

18.850 

28.2743 

7 

49 

343 

2.6458 

1.9129 

0.84510 

142.857 

21.991 

38.4845 

8 

64 

512 

2.8284 

2.0000 

0.90309 

125.000 

25.133 

50.2655 

9 

81 

729 

3.0000 

2.0801 

0.95424 

111.111 

28.274 

63.6173 

10 

100 

1000 

3.1623 

2.1544 

1.00000 

100.000 

31.416 

78.5398 

11 

121 

1331 

3.3166 

2.2240 

1.04139 

90.9091 

34.558 

95.0332 

12 

144 

1728 

3.4641 

2.2894 

1.07918 

83.3333 

37.699 

113.097 

13 

169 

2197 

3.6056 

2.3513 

1.11394 

76.9231 

40.841 

132.732 

14 

196 

2744 

3.7417 

2.4101 

.  14613 

71.4286 

43.982 

153.938 

15 

225 

3375 

3.8730 

2.4662 

.17609 

66.6667 

47.124 

176.715 

16 

256 

4096 

4.0000 

2.5198 

.20412 

62.5000 

50.265 

201.062 

17 

289 

4913 

4.1231 

2.5713 

.23045 

58.8235 

53.407 

226.980 

18 

324 

5832 

4.2426 

2.6207 

.25527 

55.5556 

56.549 

254.469 

19 

361 

6859 

4.3589 

2.6684 

.27875 

52.6316 

59.690 

283.529 

20 

400 

8000 

4.4721 

2.7144 

.30103 

50.0000 

62.832 

314.159 

21 

441 

9261 

4.5826 

2.7589 

.32222 

47.6190 

65.973 

346.361 

22 

484 

10648 

4.6904 

2.8020 

.34242 

45.4545 

69.115 

380.133 

23 

529 

12167 

4.7958 

2.8439 

.36173 

43.4783 

72.257 

415.476 

24 

576 

13824 

4.8990 

2.8845 

.38021 

41.6667 

75.398 

452.389 

25 

625 

15625 

5.0000 

2.9240 

1.39794 

40.0000 

78.540 

490.874 

26 

676 

17576 

5.0990 

2.9625 

1.41497 

38.4615 

81  .  681 

530.929 

27 

729 

19683 

5.1962 

3.0000 

1.43136 

37.0370 

84.823 

572.555 

28 

784 

21952 

5.2915 

3.0366 

1.44716 

35.7143 

87.965 

615.752 

29 

841 

24389 

5.3852 

3.0723 

1.46240 

34.4828 

91  .  106 

660.520 

30 

900 

27000 

5.4772 

3.1072 

1.47712 

33.3333 

94.248 

706.858 

31 

961 

29791 

5.5678 

3.1414 

1.49136 

32.2581 

97.389 

754.768 

32 

1024 

32768 

5.6569 

3.1748 

1.50515 

31.2500 

100.531 

804.248 

33 

1089 

35937 

5.7446 

3.2075 

1.51851 

30.3030 

103.673 

855.299 

34 

1156 

39304 

5.8310 

3.2396 

1.53148 

29.4118 

106.814 

907.920 

35 

1225 

42875 

5.9161 

3.2711 

1.54407 

28.5714 

109.956 

962.113 

36 

1296 

46656 

6.0000 

3.3019 

1.55630 

27.7778 

113.097 

1017.88 

37 

1369 

50653 

6.0828 

3.3322 

1.56820 

27.0270 

116.239 

1075.21 

38 

1444 

54872 

6.1644 

3.3620 

.57978 

26.3158 

119.381 

1134.11 

39 

1521 

59319 

6.2450 

3.3912 

.59106 

25.6410 

122.522 

1194.59 

40 

1600 

64000 

6.3246 

3.4200 

.60206 

25.0000 

125.66 

1256.64 

41 

1681 

68921 

6.4031 

3.4482 

.61278 

24.3902 

128.81 

1320.25 

42 

1764 

74088 

6.4807 

3.4760 

.62325 

23.8095 

131.95 

1385.44 

43 

1849 

79507 

6.5574 

3.5034 

.63347 

23.2558 

135.09 

1452.20 

44 

1936 

85184 

6.6332 

3.5303 

.64345 

22.7273 

138.23 

1520.53 

45 

2025 

91125 

6.7082 

3.5569 

.65321 

22.2222 

141.37 

1590.43 

46 

2116 

97336 

6.7823 

3.5830 

1.66276 

21.7391 

144.51 

1661.90 

47 

2209 

103823 

6.8557 

3.6088 

1.67210 

21  .  2766 

147.65 

1734.04 

48 

2304 

110592 

6.9282 

3.6342 

1.68124 

20.8333 

150.80 

1809.56 

49 

2401 

117649 

7.0000 

3.6593 

1.69020 

20.4082 

153.94 

1885.74 

182 


USEFUL      DATA 


FUNCTIONS  OF  NUMBERS  50  TO  99 


Square 

Cube 

1,000 

X 

No.  =  D 

AMETER 

No. 

Square 

Cube 

Root 

Root 

Logarithm 

Reciprocal 

Circum. 

Area 

50 

2500 

125000 

7.0711 

3.6840 

.69897 

20.0000 

157.08 

1963.50 

51 

2601 

132651 

7.1414 

3.7084 

.70757 

19.6078 

160.22 

2042.82 

52 

2704 

140608 

7.2111 

3.7325 

.71600 

19.2308 

163.36 

2123.72 

53 

2809 

148877 

7.2801 

3.7563 

.72428 

18.8679 

166.50 

2206.18 

54 

2916 

157464 

7.3485 

3.7798 

.73239 

18.5185 

169.65 

2290.22 

55 

3025 

166375 

7.4162 

3.8030 

.74036 

18.1818 

172.79 

2375.83 

56 

3136 

175616 

7.4833 

3.8259 

.74819 

17.8571 

175.93 

2463.01 

57 

3249 

185193 

7.5498 

3.8485 

.75587 

17.5439 

179.07 

2551.76 

58 

3364 

195112 

7.6158 

3.8708 

.76343 

17.2414 

182.21 

2642.08 

59 

3481 

205379 

7.6811 

3.8930 

.77085 

16.9492 

185.35 

2733.97 

60 

3600 

216000 

7.7460 

3.9149 

.77815 

16.6667 

188.50 

2827.43 

61 

3721 

226981 

7.8102 

3.9365 

.78533 

16.3934 

191.64 

2922.47 

62 

3844 

238328 

7.8740 

3.9579 

.79239 

16.1290 

194.78 

3019.07 

63 

3969 

250047 

7.9373 

3.9791 

.79934 

15.8730 

197.92 

3117.25 

64 

4096 

262144 

8.0000 

4.0000 

1.80618 

15.6250 

201.06 

3216.99 

65 

4225 

274625 

8.0623 

4.0207 

1.81291 

15.3846 

204.20 

3318.31 

66 

4356 

287496 

8.1240 

4.0412 

1.81954 

15.1515 

207.35 

3421  .  19 

67 

4489 

300763 

8.1854 

4.0615 

1.82607 

14.9254 

210.49 

3525.65 

68 

4624 

314432 

8.2462 

4.0817 

1.83251 

14.7059 

213.63 

3631.68 

69 

4761 

328509 

8.3066 

4.1016 

1.83885 

14.4928 

216.77 

3739.28 

70 

4900 

343000 

8.3666 

4.1213 

1.84510 

14.2857 

219.91 

3848.45 

71 

5041 

357911 

8.4261 

4.1408 

1.85126 

14.0845 

223.05 

3959.19 

72 

5184 

373248 

8.4853 

4.1602 

1.85733 

13.8889 

226.19 

4071.50 

73 

5329 

389017 

8.5440 

4.1793 

1.86332 

13.6986 

229.34 

4185.39 

74 

5476 

405224 

8.6023 

4.1983 

1.86923 

13.5135 

232.48 

4300.84 

75 

5625 

421875 

8.6603 

4.2172 

1.87506 

13.3333 

235.62 

4417.86 

76 

5776 

438976 

8.7178 

4.2358 

1.88081 

13.1579 

238.76 

4536.46 

77 

5929 

456533 

8.7750 

4.2543 

1.88649 

12.9870 

241.90 

4656.63 

78 

6084 

474552 

8.8318 

4.2727 

1.89209 

12.8205 

245.04 

4778.36 

79 

6241 

493039 

8.8882 

4.2908 

1.89763 

12.6582 

248.19 

4901.67 

80 

6400 

512000 

8.9443 

4.3089 

1.90309 

12.5000 

251.33 

5026.55 

81 

6561 

531441 

9.0000 

4.3267 

1.90849 

12.3457 

254.47 

5153.00 

82 

6724 

551368 

9.0554 

4.3445 

1.91381 

12.1951 

257.61 

5281.02 

83 

6889 

571787 

9.1104 

4.3621 

1.91908 

12.0482 

260.75 

5410.61 

84 

7056 

592704 

9.1652 

4.3795 

1.92428 

11.9048 

263.89 

5541.77 

85 

7225 

614125 

9.2195 

4.3968 

1.92942 

11.7647 

267.04 

5674.50 

86 

7396 

636056 

9.2736 

4.4140 

1.93450 

11.6279 

270.18 

5808.80 

87 

7569 

658503 

9.3274 

4.4310 

1.93952 

11.4943 

273.32 

5944.68 

88 

7744 

681472 

9.3808 

4.4480 

1.94448 

11.3636 

276.46 

6082.12 

89 

7921 

704969 

9.4340 

4.4647 

1.94939 

11.2360 

279.60 

6221.14 

90 

8100 

729000 

9.4868 

4.4814 

.95424 

11.1111 

282.74 

6361.73 

91 

8281 

753571 

9.5394 

4.4979 

.95904 

10.9890 

285.88 

6503.88 

92 

8464 

778688 

9.5917 

4.5144 

.96379 

10.8696 

289.03 

6647.61 

93 

8649 

804357 

9.6437 

4.5307 

.96848 

10.7527 

292.17 

6792.91 

94 

8836 

830584 

9.6954 

4.5468 

.97313 

10.6383 

295.31 

6939.78 

95 

9025 

857375 

9.7468 

4.5629 

.97772 

10.5263 

298.45 

7088.22 

96 

9216 

884736 

9.7980 

4.5789 

.98227 

10.4167 

301.59 

7238.23 

97 

9409 

912673 

9.8489 

4.5947 

1.98677 

10.3093 

304.73 

7389.81 

98 

9604 

941192 

9.8995 

4.6104 

1.99123 

10.2041 

307.88 

7542.96 

99 

9801 

970299 

9.9499 

4.6261 

1.99564 

10.1010 

311.02 

7697.69 

183 


CORRUGATED   BAR   COMPANY,  INC. 


DECIMALS  OF  AN  INCH  FOR  EACH 


Fractions 

Decimals 

Fractions 

Decimals 

64ths 

32nds 

leths 

8ths 

64ths 

32nds 

16ths 

8ths 

A 

0.015625 

H 

0.515625 

A 

0.03125 

H 

0.53125 

A 

0.046875 

If 

0.546875 

A 

0.0625 

A 

0.5625 

A 

0.078125 

H 

0.578125 

A 

0.09375 

H 

0.59375 

g 

0.109375 

If 

0.609375 

v% 

0.125 

N 

0.625 

_*_ 

0.140625 

I* 

0.640625 

A 

0.15625 

H 

0.65625 

_ii_ 



0.171875 

g 

_H_ 

0.671875 
0.6875 

A 

0.1875 

H 

0.203125 

if 

0.703125 

A 

0.21875 

M 

0.71875 

« 

0.234375 

H 

'0.734375 

X 

0.25 

M 

0.75 

H 

0.265625 

H 

0.765625 

4 

0.28125 

If 

0.78125 

H 

0.296875 

-H 

0.796875 

A 

0.3125 

H 



0.8125 

g 

0.328125 

« 

0.828125 

H 

0.34375 

H 

0.84375 

tt 

0.359375 

M 

0.859375 

*/8 

0.375 

K 

0.875 

g 

0.390625 

H 

0.890625 

H 

0.40625 

H 

0.90625 

H 

0.421875 

M 

0.921875 

A 

0.4375 

M 

0.9375 

« 

0.453125 

ti 

0.953125 

tt 

0.46875 

» 

0.96875 

H 

0.484375 

If 

0.984375 

y2 

0.5 

1 

1.00 

184 


USEFUL      DATA 


DECIMALS  OF  A  FOOT  FOR  EACH 


OF  AN  INCH 


In.   0" 

1" 

2" 

3" 

4" 

5" 

6" 

7" 

8" 

9" 

10" 

11" 

0 

0.0000 

0  .  0833 

0.1667 

0.2500 

0.3333 

0.4167 

0.5000 

0.5833 

0.6667 

0.7500 

0.8333 

0.9167 

A 

0.0026 

0.0859 

0.1693 

0.2526 

0.3359 

0.4193 

0.5026 

0.5859 

0.6693 

0.7526 

0.8359 

0.9193 

A 

0.0052 

0.0885 

0.1719 

0.2552 

0.3385 

0.4219 

0.5052 

0.5885 

0.6719 

0.7552 

0.8385 

0.9219 

ft 

0.0078 

0.0911 

0.1745 

0.2578 

0.3411 

0.4245 

0.5078 

0.5911 

0  .  6745 

0.7578 

0.8411 

0.9245 

K 

0.0104 

0.0937 

0.1771 

0.2604 

0.3437 

0.4271 

0.5104 

0.5937 

0.6771 

0.7604 

0.8437 

0.9271 

A 

0.0130 

0.0964 

0.1797 

0.2630 

0.3464 

0.4297 

0.5130 

0.5964 

0.6797 

0.7630 

0.8464 

0.9297 

A 

0.0156 

0.0990 

0.1823 

0.2656 

0.3490 

0.4323 

0.5156 

0.5990 

0.6823 

0.7656 

0.8490 

0.9323 

A 

0.0182 

0.1016 

0.1849 

0.2682 

0.3516 

0.4349 

0.5182 

0.6016 

0  .  6849 

0.7682 

0.8516 

0.9349 

U 

0.0208 

0.1042 

0.1875 

0.2708 

0.3542 

0.4375 

0.5208 

0.6042 

0.6875 

0.7708 

0.8542 

0.9375 

ft 

0.0234 

0.1068 

0.1901 

0.2734 

0.3568 

0.4401 

0.5234 

0.6068 

0.6901 

0.7734 

0.8568 

0.9401 

A 

0.0260 

0.1094 

0.1927 

0.2760 

0.3594 

0.4427 

0.5260 

0.6094 

0.6927 

0.7760 

0.8594 

0.9427 

H 

0.0286 

0.1120 

0.1953 

0.2786 

0.3620 

0.4453 

0.5286 

0.6120 

0.6953 

0.7786 

0.8620 

0.9453 

H 

0.0312 

0.1146 

0.1979 

0.2812 

0.3646 

0.4479 

0.5312 

0.6146 

0.6979 

0.7812 

0.8646 

0.9479 

H 

0.0339 

0.1172 

0.2005 

0.2839 

0.3672 

0.4505 

0.5339 

0.6172 

0.7005 

0.7839 

0.8672 

0.9505 

A 

0  .  0365 

0.1198 

0.2031 

0.2865 

0.3698 

0.4531 

0.5365 

0.6198 

0.7031 

0.7865 

0.8698 

0.9531 

if 

0.0391 

0,.  1224 

0.2057 

0.2891 

0.3724 

0.4557 

0.5391 

0.6224 

0.7057 

0.7891 

0.8724 

0.9557 

H 

0.0417 

0.1250 

0.2083 

0.2917 

0.3750 

0.4583 

0.5417 

0.6250 

0.7083 

0.7917 

0.8750 

0.9583 

H 

0.0443 

0.1276 

0.2109 

0.2943 

0.3776 

0.4609 

0  .  5443 

0.6276 

0.7109 

0.7943 

0.8776 

0.9609 

A 

0.0469 

0.1302 

0.2135 

0.2969 

0.3802 

0.4635 

0.5469 

0.6302 

0.7135 

0.7969 

0.8802 

0.9635 

H 

0.0495 

0.1328 

0.2161 

0.2995 

0.3828 

0.4661 

0.5495 

0.6328 

0.7161 

0.7995 

0.8828 

0.9661 

H 

0.0521 

0.1354 

0.2188 

0.3021 

0.3854 

0.4688 

0.5521 

0.6354 

0.7188 

0.8021 

0.8854 

0.9688 

H 

0.0547 

0.1380 

0.2214 

0.3047 

0.3880 

0.4714 

0.5547 

0.6380 

0.7214 

0.8047 

0.8880 

0.9714 

H 

0.0573 

0.1406 

0.2240 

0.3073 

0.3906 

0.4740 

0.5573 

0.6406 

0.7240 

0  .  8073 

0.8906 

0.9740 

B 

0.0599 

0  .  1432 

0.2266 

0.3099 

0.3932 

0.4766 

0.5599 

0.6432 

0.7266 

0.8099 

0.8932 

0.9766 

X 

0.0625 

0.1458 

0.2292 

0.3125 

0.3958 

0.4792 

0  .  5625 

0.6458 

0.7292 

0.8125 

0.8958 

0.9792 

II 

0.0651 

0.1484 

0.2318 

0.3151 

0.3984 

0.4818 

0.5651 

0.6484 

0.7318 

0.8151 

0.8984 

0.9818 

if 

0  .  0677 

0.1510 

0.2344 

0.3177 

0.4010 

0.4844 

0.5677 

0.6510 

0.7344 

0.8177 

0.9010 

0.9844 

& 

0.0703 

0.1536 

0.2370 

0.3203 

0.4036 

0.4870 

0.5703 

0.6536 

0.7370 

0  .  8203 

0.9036 

0.9870 

W 

0.0729 

0.1562 

0.2396 

0  .  3229 

0.4062 

0.4896 

0.5729 

0.6562 

0.7396 

0.8229 

0.9062 

0.9896 

ft 

0.0755 

0.1589 

0.2422 

0.3255 

0.4089 

0.4922 

0.5755 

0.6589 

0.7422 

0.8255 

0.9089 

0.9922 

H 

0.0781 

0.1615 

0.2448 

0.3281 

0.4115 

0.4948 

0.5781 

0.6615 

0.7448 

0.8281 

0.9115 

0.9948 

H 

0  .  0807 

0.1641 

0.2474 

0.3307 

0.4141 

0.4974 

0.5807 

0.6641 

0.7474 

0.8307 

0.9141 

0.9974 

i 

1.0000 

185 


CORRUGATED   BAR   COMPANY,  INC. 


AMERICAN  SOCIETY  FOR  TESTING  MATERIALS 

PHILADELPHIA,  PA.,  U.  S.  A. 

AFFILIATED  WITH  THE 
INTERNATIONAL  ASSOCIATION  FOR  TESTING  MATERIALS 

STANDARD  SPECIFICATIONS  FOR  PORTLAND   CEMENT 

ADOPTED,  1904;  REVISED,  1908,  1909,  1916,  1918  STANDARD. 

Portland  cement  is  the  product  obtained  by  finely  pulverizing  clinker  produced 
by  calcining  to  incipient  fusion,  an  intimate  and  properly  proportioned  mixture  of 
argillaceous  and  calcareous  materials,  with  no  additions  subsequent  to  calcination 
excepting  water  and  calcined  or  uncalcined  gypsum. 

I.  CHEMICAL  PROPERTIES 
Chemical  Limits.     The  following  limits  shall  not  be  exceeded: 

Loss  on  ignition,  per  cent 4 . 00 

Insoluble  residue,  per  cent 0 . 85 

Sulf uric  anhydride  (SO3),  per  cent 2.00 

Magnesia  (MgO),  per  cent 5.00 

II.  PHYSICAL  PROPERTIES 

Specific  Gravity.  The  specific  gravity  of  cement  shall  be  not  less  than  3.10 
(3.07  for  white  Portland  cement).  Should  the  test  of  cement  as  received  fall  below 
this  requirement  a  second  test  may  be  made  upon  an  ignited  sample.  The  specific 
gravity  test  will  not  be  made  unless  specifically  ordered. 

Fineness.  The  residue  on  a  standard  No.  200  sieve  shall  not  exceed  22  per  cent 
by  weight. 

Soundness.  A  pat  of  neat  cement  shall  remain  firm  and  hard,  and  show  no  signs 
of  distortion,  cracking,  checking,  or  disintegration  in  the  steam  test  for  soundness. 

Time  of  Setting.  The  cement  shall  not  develop  initial  set  in  less  than  45  minutes 
when  the  Vicat  needle  is  used,  or  60  minutes  when  the  Gillmore  needle  is  used.  Final 
set  shall  be  attained  within  10  hours. 

Tensile  Strength.  The  average  tensile  strength  in  pounds  per  square  inch  of  not 
less  than  three  standard  mortar  briquettes  composed  of  one  part  cement  and  three 
parts  standard  sand,  by  weight,  shall  be  equal  to  or  higher  than  the  following: 


Age  at  Test 
Days 

Storage  of  Briquettes 

Tensile  Strength 
Ib.  per  sq.  in. 

7 
28 

Iday 
1  day 

in  moist  air,    6  days  in  water 
in  moist  air,  27  days  in  water 

200 
300 

The  average  tensile  strength  of  standard  mortar  at  28  days  shall  be  higher  than 
the  strength  at  7  days. 

III.  PACKAGES,  MARKING  AND  STORAGE 

Packages  and  Marking.  The  cement  shall  be  delivered  in  suitable  bags  or  barrels 
with  the  brand  and  name  of  the  manufacturer  plainly  marked  thereon,  unless  shipped 
in  bulk.  A  bag  shall  contain  94  Ib.  net.  A  barrel  shall  contain  376  Ib.  net. 

186 


USEFUL      DATA 


Storage.  The  cement  shall  be  stored  in  such  a  manner  as  to  permit  easy  access 
for  proper  inspection  and  identification  of  each  shipment,  and  in  a  suitable  weather- 
tight  building  which  will  protect  the  cement  from  dampness. 

IV.  INSPECTION 

Inspection.  Every  facility  shall  be  provided  the  purchaser  for  careful  sampling 
and  inspection  at  either  the  mill  or  at  the  site  of  the  work,  as  may  be  specified  by  the 
purchaser.  At  least  10  days  from  the  time  of  sampling  shall  be  allowed  for  the  com- 
pletion of  the  7-day  test,  and  at  least  31  days  shall  be  allowed  for  the  completion  of 
the  28-day  test.  The  cement  shall  be  tested  in  accordance  with  the  methods  herein- 
after prescribed.  The  28-day  test  shall  be  waived  only  when  specifically  so  ordered. 

V.  REJECTION 

Rejection.  The  cement  may  be  rejected  if  it  fails  to  meet  any  of  the  requirements 
of  these  specifications. 

Cement  shall  not  be  rejected  on  account  of  failure  to  meet  the  fineness  requirement 
if  upon  retest  after  drying  at  100  degrees  C.  for  one  hour  it  meets  this  requirement. 

Cement  failing  to  meet  the  test  for  soundness  in  steam  may  be  accepted  if  it  passes 
a  retest  using  a  new  sample  at  any  time  within  28  days  thereafter. 

Packages  varying  more  than  5  per  cent  from  the  specified  weight  may  be  rejected; 
and  if  the  average  weight  of  packages  in  any  shipment,  as  shown  by  weighing  50 
packages  taken  at  random,  is  less  than  that  specified,  the  entire  shipment  may  be 
rejected. 


187 


CORRUGATED   BAR   COMPANY,  INC. 


MANUFACTURERS'  STANDARD  SPECIFICATIONS  FOR 

DEFORMED  CONCRETE  REINFORCEMENT  BARS 

ROLLED  FROM  BILLETS 

REVISED  APRIL  21,  1914 

Manufacture.  Steel  may  be  made  by  either  the  open-hearth  or  Bessemer  process. 
Bars  shall  be  rolled  from  standard  new  billets. 

Chemical  and  Physical  Properties.  The  chemical  and  physical  properties 
shall  conform  to  the  following  limits: 


Properties  Considered 

Structural 
Grade 

Intermediate 
Grade 

Hard 
Grade 

PHOSPHORUS,  maximum, 
Bessemer                                        .    . 

0.10 

0.06 
55-70,000 

33,000 
1,250,000 

0.10 
0.06 

70-85,000 

40,000 
1,125,000 

0.10 
0.06 

80,000  min. 

50,000 
1,000,000 

Open-hearth                           

Ultimate  tensile  strength,  Ib.  per  sq.  in.     . 
Yield  point,  minimum,  Ib.  per  sq.  in.     .    . 
Elongation,  per  cent  in  8-in.,  minimum 

COLD  BEND  WITHOUT  FRACTURE: 
Bars  under  %-in.  in  diameter  or  thickness 

Bars  %-in.  in  diameter  or  thickness  and 
over 

Tens.  Str. 
180°  d.  =  lt 

180°d.  =  2/. 

Tens.  Str. 
180°d  =  3/. 

90°d.  =  3*. 

Tens.  Str. 
180°d=4*. 

90°d.  =  4*. 

The  intermediate  and  hard  grades  will  be  used  only  when  specified. 

Chemical  Determinations.  In  order  to  determine  if  the  material  conforms  to 
the  chemical  limitations  prescribed  in  the  preceding  tables,  analysis  shall  be  made  by 
the  manufacturer  from  a  test  ingot  taken  at  the  time  of  the  pouring  of  each  melt  or 
blow  of  steel,  and  a  correct  copy  of  such  analysis  shall  be  furnished  to  the  engineer  or 
his  inspector. 

Yield  Point.  For  the  purposes  of  these  specifications,  the  yield  point  shall  be 
determined  by  careful  observation  of  the  drop  of  the  beam  of  the  testing  machine,  or 
by  other  equally  accurate  method. 

Form  of  Specimens.  Tensile  and  bending  test  specimens  may  be  cut  from 
the  bars  as  rolled,  but  tensile  and  bending  test  specimens  of  deformed  bars  may 
be  planed  or  turned  for  a  length  of  at  least  nine  inches  if  deemed  necessary  by  the 
manufacturer  in  order  to  obtain  uniform  cross-section. 

Number  of  Tests,  (a) — At  least  one  tensile  and  one  bending  test  shall  be  made 
from  each  melt  of  open-hearth  steel  rolled,  and  from  each  blow  or  lot  of  ten  tons  of 
Bessemer  steel  rolled.  In  case  bars  differing  ^g-inch  and  more  in  diameter  or  thick- 
ness are  rolled  from  one  melt  or  blow,  a  test  shall  be  made  from  the  thickest  and 
thinnest  material  rolled.  Should  either  of  these  test  specimens  develop  flaws,  or  should 
the  tensile  test  specimen  break  outside  of  the  middle  third  of  its  gauged  length,  it 
may  be  discarded  and  another  test  specimen  substituted  therefor.  In  case  a  tensile 
test  specimen  does  not  meet  the  specifications,  an  additional  test  may  be  made. 

(6) — The  bending  test  may  be  made  by  pressure  or  by  light  blows. 

188 


USEFUL      DATA 


Modifications  in  Elongation  for  Thin  and  Thick  Material.  For  bars  less  than 
3^-inch  and  more  than  %-inch  nominal  diameter  or  thickness,  the  following  modifi- 
cations shall  be  made  in  the  requirements  for  elongation: 

(a) — For  each  increase  of  J's-mch  in  diameter  or  thickness  above  %-inch,  a  deduc- 
tion of  1  shall  be  made  from  the  specified  percentage  of  elongation. 

(6) — For  each  decrease  of  j^-inch  in  diameter  or  thickness  below  y^-inch,  a  deduc- 
tion of  1  shall  be  made  from  the  specified  percentage  of  elongation. 

Finish.  Material  must  be  free  from  injurious  seams,  flaws  or  cracks,  and  have  a 
workmanlike  finish. 

Variation  in  Weight.  Bars  for  reinforcement  are  subject  to  rejection  if  the 
actual  weight  of  any  lot  varies  more  than  5  per  cent  over  or  under  the  theoretical 
weight  of  that  lot. 

NOTE: — The  chemical  and  physical  properties  are  given  for  three  different  grades  of  steel.  In 
using  the  specification  care  should  be  taken  to  indicate  clearly  the  grade  desired. 


189 


CORRUGATED      BAR      COMPANY,     INC. 


GENERAL  SPECIFICATIONS  FOR  MATERIALS  AND  LABOR 
USED  IN  REINFORCED  CONCRETE  CONSTRUCTION 

MATERIALS 

Cement.  The  cement  used  for  reinforced  concrete  construction  shall  be  Portland 
cement  which  shall  meet  the  requirements  of  the  specifications  and  methods  of  tests 
last  adopted  by  the  American  Society  for  Testing  Materials. 

Aggregates,  (a)  Fine. — Fine  aggregates  shall  consist  of  uniformly  graded  sand 
or  screenings  by  particles  not  exceeding  J^-inch  in  diameter;  not  more  than  30  per 
cent  by  weight  shall  pass  a  sieve  having  50  meshes  per  linear  inch. 

Particles  shall  be  hard  and  clean;  shall  be  free  from  coatings  and  soluble  substances; 
shall  contain  no  vegetable  loam  or  other  organic  matter;  and  shall  yield  a  1 :3  mortar 
of  a  strength  at  the  age  of  seven  days  of  not  less  than  70  per  cent  of  that  of  1 :3  mortar 
of  the  same  consistency  and  made  with  the  same  cement  and  standard  Ottawa  sand. 

(6)  Coarse. — Coarse  aggregates  shall  consist  of  gravel  or  crushed  stone  which  is 
retained  on  a  screen  having  3<£-inch  diameter  holes  and  shall  be  graded  from  the 
smallest  to  the  largest  particles.  The  maximum  size  of  particles  shall  be  determined 
from  the  following  table: 

Nature  of  work                                           Maximum  Sizes  in  Inches 
Light  slabs  or  partitions  using  mesh  or  expanded  metal     .    .       3/£ 
Flat  Slab  Floors,  Beams  and  Slabs,  Girders,  Columns,  Re- 
taining Walls,  Footings  and  other  moderately  heavy  work       % 
Heavy  work 1% 

Size  and  quality  of  stone  for  rubble  concrete  shall  meet  the  approval  of  the  Engineer. 

All  coarse  aggregates  shall  be  clean,  hard,  durable,  free  from  coatings  and  all  delete- 
rious matter. 

Water.  The  water  used  in  mixing  concrete  shall  be  free  from  oil,  acid,  alkali 
or  organic  matter.  Concrete  shall  not  be  mixed  with  sea  water. 

Metal  Reinforcement.  Bars  used  as  reinforcement  in  reinforced  concrete  work 
shall  be  manufactured  from  new  billet-steel  and  shall  satisfy  the  specifications  known 
as  the  Manufacturers'  Standard  Specifications  for  Billet-Steel  Concrete  Reinforcement 
Bars.  All  bars  other  than  spiral  wire  shall  be  an  approved  deformed  bar  having  a 
positive  mechanical  bond  with  the  concrete  equal  to  that  of  the  Corrugated  Bar, 
manufactured  by  the  Corrugated  Bar  Company,  Inc.,  Buffalo,  N.  Y. 

FORMS 

Character.  Forms  for  reinforced  concrete  construction  shall  be  substantial  and 
unyielding,  and  shall  conform  to  the  design  of  the  structure.  They  shall  have  a  smooth 
surface  in  contact  with  the  concrete,  which  shall  be  free  from  adhering  material  or 
from  other  defects  which  shall  mar  the  finished  surface.  They  shall  be  sufficiently 
tight  to  prevent  the  leakage  of  mortar. 

The  forms  shall  be  so  made  that  all  interior  angles  caused  by  the  junction  of  slabs 
and  beams  or  other  members  shall  be  chamfered  one  inch.  All  exterior  angles  shall  be 
made  square. 

Oiling  and  Inspection.  Before  placing  the  concrete  in  the  forms,  all  debris  in 
the  space  to  be  occupied  by  the  concrete  shall  be  removed.  Handholes  shall  be  pro- 
vided at  the  base  of  the  forms  of  all  columns  to  render  this  space  accessible  for  cleaning. 

190 


USEFUL      DATA 


The  forms  shall  be  thoroughly  oiled  (thin  mineral  oil)  before  the  concrete  is  placed; 
or  the  sin-face  shall  be  thoroughly  wetted  (excepting  in  freezing  weather). 

PLACING  OF  REINFORCEMENT 

All  reinforcement  shall  be  placed  in  accordance  with  the  plans  furnished  by  the 
Engineer. 

All  loose  rust  or  scale,  all  adhering  material,  and  all  oil  or  other  substance  which 
will  tend  to  destroy  bonding  between  the  concrete  and  the  reinforcement  shall  be 
removed  before  pouring  begins. 

MIXING  OF  CONCRETE 

Mixing  shall  be  done  in  a  batch  machine  mixer  of  a  type  which  will  insure  uniform 
distribution  of  the  materials  throughout  the  mass,  and  shall  continue  for  the  minimum 
time  of  one  and  one-half  minutes  after  all  ingredients  are  assembled  in  the  mixer. 
For  mixers  of  two  or  more  cubic  yards  capacity  the  minimum  time  of  mixing  shall  be 
two  minutes.  The  drum  of  the  machine  shall  be  operated  at  a  uniform  speed  of  200 
feet  per  minute. 

Unit  of  Measure.  Measurements  of  fine  and  coarse  aggregates  and  of  cement, 
shall  be  by  loose  volume.  The  unit  of  measure  shall  be  a  bag  of  cement  containing 
94  pounds  net,  which  should  be  considered  the  equivalent  of  one  cubic  foot. 

Proportioning.  The  fine  and  coarse  aggregates  shall  be  so  proportioned  with 
the  cement  as  to  secure  the  ultimate  compressive  strength,  in  twenty-eight  days,  upon 
which  the  design  of  the  structure  was  based. 

The  following  table  is  recommended  as  the  maximum  ultimate  compressive  strength 
of  different  mixtures  of  concrete  at  twenty-eight  days: 

TABLE  OF   COMPRESSIVE  STRENGTHS  OF  DIFFERENT 
MIXTURES  OF  CONCRETE 

(In  Pounds  per  Square  Inch) 


Aggregate 

1:3* 

1:4H* 

1:6* 

1:7H* 

1:9* 

Granite,  trap  rock      
Gravel,  hard  limestone  and  hard  sandstone  .    .    . 
Soft  limestone  and  sandstone  

3300 
3000 
2200 

2800 
2500 
1800 

2200 
2000 
1500 

1800 
1600 
1200 

1400 
1300 
1000 

Cinders     

800 

700 

600 

500 

400 

Consistency.  The  materials  shall  be  mixed  wet  enough  to  produce  a  concrete  of 
such  consistency  as  will  flow  sluggishly  into  the  forms  and  about  the  metal  reinforce- 
ment, and  which  at  the  same  time  can  be  conveyed  from  the  mixer  to  the  forms  with- 
out separation  of  the  coarse  aggregate  from  the  mortar.  A  properly  mixed  concrete  is 
one  which  thoroughly  sustains  or  supports  the  coarser  aggregate  throughout  the  mass 
and  which  when  dumped  from  a  barrel  or  buggy  neither  breaks  nor  flows  readily  over 
the  edge. 

Retempering.  The  remixing  of  mortar  or  concrete  that  has  partly  set  shall  not 
be  permitted. 


*The  proportions  here  given  are  on  the  basis  of  separately  measured  aggregates.  For  instance;  a 
1:6  mixture  refers  to  a  mixture  based  on  one  part  of  cement  and  six  parts  of  aggregates  which  were 
measured  before  being  combined.  A  standard  1 :2:4  mix,  therefore,  falls  in  the  above  class  of  1:6  mix. 


191 


CORRUGATED   BAR   COMPANY,  INC. 


Conveying  and  Placing.  After  the  mixing  of  the  concrete  has  been  completed, 
it  shall  be  conveyed  as  rapidly  as  possible  to  the  place  of  deposit.  No  concrete  shall 
be  placed  which  has  partly  set.  Where  concrete  is  conveyed  by  spouting,  the  plant 
shall  be  of  such  size  and  design  as  to  insure  a  practically  continuous  flow  in  the  spout. 
The  angle  of  the  spout  shall  be.  such  as  to  allow  the  concrete  to  flow  without  a  separa- 
tion of  the  ingredients.  The  spout  shall  be  thoroughly  cleaned  by  flushing  before  and 
after  each  run.  Where  it  is  impossible  to  deliver  the  concrete  at  the  place  of  deposit 
without  separation  of  the  ingredients,  the  concrete  shall  be  discharged  upon  a  mixing 
board  where  it  shall  be  mixed  by  turning  until  of  uniform  consistency  before  placing 
in  the  forms. 

The  concrete  shall  be  deposited  in  the  forms  in  such  a  manner  as  will  permit  the 
most  thorough  compacting  obtained  by  working  with  a  straight  shovel  or  slicing 
tool  kept  moving  up  and  down  until  all  the  ingredients  are  in  their  proper  place. 

Light  horizontal  reinforcement  shall  be  raised  from  the  bottom  forms  to  allow  the 
flow  of  the  concrete  under  it.  Where  chairs  are  used,  or  where  heavy  reinforcement 
is  definitely  wired  in  place,  the  mass  shall  be  thoroughly  worked  to  insure  contact  of 
the  mortar  with  the  lower  face  of  the  reinforcing  material. 

Before  concrete  is  placed  upon  previously  poured  concrete,  care  shall  be  taken  to 
remove  all  debris  from  the  concrete  surface.  All  laitance  shall  be  removed  and  the 
surface  shall  be  thoroughly  wetted  and  slushed  with  mortar  consisting  of  one  part 
Portland  cement  and  two  parts  fine  aggregate. 

When  it  is  necessary  to  stop  pouring  at  a  place  where  pouring  will  be  resumed  at  a 
later  date,  all  necessary  grooves  for  joining  future  work  shall  be  made  before  the  con- 
crete has  set. 

Construction  Joints.  Construction  joints  in  columns  shall  be  located  at  the  base 
of  the  bell  or  flare  occurring  immediately  below  the  floor  slab  in  flat  slab  construction. 
In  beam  and  girder  construction  the  joint  in  the  columns  shall  be  located  at  the  base 
of  the  lowest  intersecting  member  at  each  floor. 

Vertical  joints  formed  by  bulkheads  which  it  may  be  necessary  to  construct  in  slab 
or  beams  shall  be  made  at  the  center  of  the  span  of  such  slab  or  beam.  In  girders  into 
which  intersecting  members  are  framed  at  the  center  of  the  span,  the  bulkhead  shall 
be  located  within  the  middle  third  of  the  length  of  the  span  of  such  girder.  On  large 
beams  or  girders  these  bulkheads  shall  be  placed  inclined  upward  toward  the  nearest 
column. 

Horizontal  joints  in  large  girders  or  other  massive  units  shall  be  properly  keyed  by 
notching. 

Lintel  beams,  whether  above  or  below  the  slab,  shall  be  poured  monolithically  with 
the  slab. 

No  construction  joints  shall  be  allowed  in  footings,  the  pouring  to  be  continued  until 
the  whole  footing  is  completed  to  the  base  of  the  column. 

All  other  joints  in  pouring  shall  be  made  only  upon  the  approval  of  the  Engineer. 

Placing  Concrete  in  Freezing  Weather.  No  concrete  shall  be  mixed  or  placed 
at  a  freezing  temperature  unless  special  precautions  are  taken  to  prevent  the  use  of 
materials  covered  with  ice  crystals  or  containing  frost,  and  to  prevent  the  concrete 
from  freezing  before  it  has  set  and  sufficiently  hardened. 

The  material  used  shall  be  warmed  well  above  the  freezing  point  and  the  space  of 

192 


USEFUL      DATA 


the  structure  in  which  pouring  is  taking  place  shall  be  maintained  at  a  temperature 
well  above  the  freezing  point.  Aggregates  and  water  used  shall  not  be  heated  to  more 
than  70  degrees.  The  use  of  salt  to  lower  the  freezing  point  shall  not  be  permitted. 

Placing  Concrete  Under  Water.  Concrete  may  be  placed  only  in  still  water, 
with  the  use  of  a  tremie  properly  designed  and  operated.  Concrete  shall  be  mixed  with 
more  water  than  is  ordinarily  permissible  so  that  it  will  flow  readily  through  the  tremie. 
Coarse  aggregate  used  in  concrete  thus  placed  shall  not  be  more  than  one  inch  in 
diameter. 

In  case  the  flow  of  concrete  is  interrupted,  or  in  case  it  is  necessary  to  provide  a 
construction  joint,  care  shall  be  taken  to  remove  all  laitance  before  proceeding  with 
the  work. 

Protection  of  Exposed  Surfaces.  The  surfaces  of  concrete  exposed  to  prema- 
ture drying  shall  be  covered  and  kept  wet  for  a  period  of  at  least  seven  days  after 
pouring. 

REMOVAL  OF  FORMS 

Fornis  shall  not  be  removed  from  the  concrete  until  it  is  sufficiently  hard  to  permit 
of  this  being  done  with  safety. 

In  weather  of  a  temperature  above  60  degrees,  the  minimum  time  after  pouring  for 
the  removal  of  forms  shall  be  as  follows: 

Wall  forms  and  forms  for  the  sides  of  beams 2  days 

Column  forms  and  forms  under  slabs  of  span  less  than  4  feet     .    4  days 

Slabs  of  span  between  supported  girders  or  shoring  between  4  and 

10  feet 6  days 

Supports  or  shoring  shall  be  maintained  under  horizontal  members  a  minimum  time 
after  pouring  in  accordance  with  the  following  table: 

Beams,  Girders  and  Flat  Slabs  in  ordinary  building  construction  .    3  weeks 
Spans  over  30  feet At  least   1  month 

Under  all  floors  upon  which  building  materials  are  being  placed  during  construc- 
tion, the  supports  or  posts  shall  be  left  at  least  two  weeks  longer  than  specified  in  the 
above  schedules. 

In  weather  of  a  temperature  below  60  degrees,  the  forms  and  supports  shall  be  left 
in  place  a  longer  period,  depending  upon  the  weather  encountered. 

Especial  care  shall  be  taken  in  the  removal  of  forms  from  any  concrete  that  may 
have  become  frozen.  Where  it  is  likely  that  the  concrete  might  have  frozen,  it  may  be 
tested  by  placing  a  piece  of  the  concrete  in  warm  water  or  upon  a  stove,  after  which, 
if  the  concrete  is  properly  set,  it  shall  not  show  any  deterioration  due  to  such  treatment. 
A  similar  test  may  be  made  directly  upon  the  structure  by  submitting  it  to  the  flame 
of  a  blow  torch,  which  treatment  will  not  produce  any  melting,  if  the  concrete  is 
properly  set.  If  the  concrete  has  frozen,  the  forms  shall  not  be  removed  from  it  until 
it  has  had  sufficient  time  to  thoroughly  thaw  and  set  in  warm  weather. 


193 


CORRUGATED      BAR      COMPANY,     INC. 


RECOMMENDATIONS  ON  DESIGN  AND  WORKING 
STRESSES    IN    REINFORCED    CON- 
CRETE CONSTRUCTION. 

(From  the  Final  Report  of  the  Joint  Committee  on  Concrete  and  Reinforced  Concrete, 

July  1,  1916) 

Massive  Concrete.  In  the  design  of  massive  or  plain  concrete,  no  account  should 
be  taken  of  the  tensile  strength  of  the  material,  and  sections  should  usually  be  pro- 
portioned so  as  to  avoid  tensile  stresses  except  in  slight  amounts  to  resist  indirect 
stresses.  This  will  generally  be  accomplished  in  the  case  of  rectangular  shapes  if  the 
line  of  pressure  is  kept  within  the  middle  third  of  the  section,  but  in  very  large  struc- 
tures, such  as  high  masonry  dams,  a  more  exact  analysis  may  be  required.  Structures 
of  massive  concrete  are  able  to  resist  unbalanced  lateral  forces  by  reason  of  their 
weight;  hence  the  element  of  weight  rather  than  strength  often  determines  the 
design.  A  leaner  and  relatively  cheap  concrete,  therefore,  will  often  be  suitable  for 
massive  concrete  structures. 

It  is  desirable  generally  to  provide  joints  at  intervals  to  localize  the  effect  of  con- 
traction. 

Massive  concrete  is  suitable  for  dams,  retaining  walls,  and  piers  in  which  the  ratio 
of  length  to  least  width  is  relatively  small.  Under  ordinary  conditions  this  ratio 
should  not  exceed  four.  It  is  also  suitable  for  arches  of  moderate  span. 

Reinforced  Concrete.  The  use  of  metal  reinforcement  is  particularly  advanta- 
geous in  members  such  as  beams  in  which  both  tension  and  compression  exist,  and  in 
columns  where  the  principal  stresses  are  compressive  and  where  there  also  may  be 
cross-bending.  Therefore,  the  theory  of  design  here  presented  relates  mainly  to  the 
analysis  of  beams  and  columns. 

General  Assumptions,     (a)  Loads.— The  forces  to  be  resisted  are  those  due  to: 

1.  The  dead  load,  which  includes  the  weight  of  the  structure  and  fixed  loads  and  forces. 

2.  The  live  load,  or  the  loads  and  forces  which  are  variable.   The  dynamic  effect  of 
the  live  load  will  often  require  consideration.    Allowance  for  the  latter  is  preferably 
made  by  a  proportionate  increase  in  either  the  live  load  or  the  live  load  stresses.  The 
working  stresses  hereinafter  recommended  are  intended  to  apply  to  the  equivalent 
static  stresses  thus  determined. 

In  the  case  of  high  buildings  the  live  load  on  columns  may  be  reduced  in  accordance 
with  the  usual  practice. 

(6)  Lengths  of  Beams  and  Columns. — The  span  length  for  beams  and  slabs  simply 
supported  should  be  taken  as  the  distance  from  center  to  center  of  supports,  but  need 
not  be  taken  to  exceed  the  clear  span  plus  the  depth  of  beam  or  slab.  For  continuous 
or  restrained  beams  built  monolithically  into  supports  the  span  length  may  be  taken 
as  the  clear  distance  between  faces  of  supports.  Brackets  should  not  be  considered  as 
reducing  the  clear  span  in  the  sense  here  intended,  except  that  when  brackets  which 
make  an  angle  of  45  degrees  or  more  with  the  axis  of  a  restrained  beam  are  built  mono- 
lithically with  the  beam,  the  span  may  be  measured  from  the  section  where  the  com- 
bined depth  of  beam  and  bracket  is  at  least  one-third  more  than  the  depth  of  the 
beam.  Maximum  negative  moments  are  to  be  considered  as  existing  at  the  end  of  the 
span  as  here  defined. 

194 


USEFUL,      DATA 


When  the  depth  of  a  restrained  beam  is  greater  at  its  ends  than  at  midspan  and  the 
slope  of  the  bottom  of  the  beam  at  its  ends  makes  an  angle  of  not  more  than  15  degrees 
with  the  direction  of  the  axis  of  the  beam  at  midspan,  the  span  length  may  be  measured 
from  face  to  face  of  supports. 

The  length  of  columns  should  be  taken  as  the  maximum  unstayed  length. 

(c)  Stresses. — The  following  assumptions  are  recommended  as  a  basis  for  calculations: 

1. — Calculations  will  be  made  with  reference  to  working  stresses  and  safe  loads 
rather  than  with  reference  to  ultimate  strength  and  ultimate  loads. 

2. — A  plane  section  before  bending  remains  plane  after  bending. 

3. — The  modulus  of  elasticity  of  concrete  in  compression  is  constant  within  the 
usual  limits  of  working  stresses.  The  distribution  of  compressive  stress  in  beams  is, 
therefore,  rectilinear. 

4. — In  calculating  the  moment  of  resistance  of  beams  the  tensile  stresses  in  the 
concrete  are  neglected. 

5. — The  adhesion  between  the  concrete  and  the  reinforcement  is  perfect.  Under 
compressive  stress  the  two  materials  are,  therefore,  stressed  in  proportion  to  their 
moduli  of  elasticity. 

6. — The  ratio  of  the  modulus  of  elasticity  of  steel  to  the  modulus  of  elasticity  of 
concrete  is  taken  at  15,  except  as  modified  in  section  on  "Working  Stresses." 

7  — Initial  stress  in  the  reinforcement  due  to  contraction  or  expansion  of  the  concrete 
is  neglected. 

It  is  recognized  that  some  of  the  assumptions  given  herein  are  not  entirely  borne  out 
by  experimental  data.  They  are  given  in  the  interest  of  simplicity  and  uniformity, 
and  variations  from  exact  conditions  are  taken  into  account  in  the  selection  of  formulas 
and  working  stresses. 

The  deflection  of  a  beam  depends  upon  the  strength  and  stiffness  developed 
throughout  its  length.  For  calculating  deflection  a  value  of  8  for  the  ratio  of  the 
moduli  will  give  results  corresponding  approximately  with  the  actual  conditions. 

T-Beams.  In  beam  and  slab  construction  an  effective  bond  should  be  provided  at 
the  junction  of  the  beam  and  slab.  When  the  principal  slab  reinforcement  is 
parallel  to  the  beam,  transverse  reinforcement  should  be  used  extending  over  the 
beam  and  well  into  the  slab. 

The  slab  may  be  considered  an  integral  part  of  the  beam,  when  adequate  bond  and 
shearing  resistance  between  slab  and  web  of  beam  is  provided,  but  its  effective  width 
shall  be  determined  by  the  following  rules : 

(a) — It  shall  not  exceed  one-fourth  of  the  span  length  of  the  beam; 

(6) — Its  overhanging  width  on  either  side  of  the  web  shall  not  exceed  six  times  the 
thickness  of  the  slab. 

In  the  design  of  continuous  T-beams,  due  consideration  should  be  given  to  the  com- 
pressive stress  at  the  support. 

Beams  in  which  the  T-form  is  used  only  for  the  purpose  of  providing  additional 
compression  area  of  concrete  should  preferably  have  a  width  of  flange  not  more  than 
three  times  the  width  of  the  stem  and  a  thickness  of  flange  not  less  than  one-third  of 
the  depth  of  the  beam.  Both  in  this  form  and  in  the  beam  and  slab  form  the  web 
stresses  and  the  limitations  in  placing  and  spacing  the  longitudinal  reinforcement  will 
probably  be  controlling  factors  in  design. 

195 


CORRUGATED      BAR      COMPANY,     INC. 


Floor  Slabs  Supported  Along  Four  Sides.  Floor  slabs  having  the  supports 
extending  along  the  four  sides  should  be  designed  and  reinforced  as  continuous  over 
the  supports.  If  the  length  of  the  slab  exceeds  1.5  times  its  width  the  entire  load  should 
be  carried  by  transverse  reinforcement. 

For  uniformly  distributed  loads  on  square  slabs,  one-half  the  live  and  dead  load 
may  be  used  in  the  calculations  of  moment  to  be  resisted  in  each  direction.  For  oblong 
slabs,  the  length  of  which  is  not  greater  than  one  and  one-half  times  their  width,  the 
moment  to  be  resisted  by  the  transverse  reinforcement  may  be  found  by  using  a  pro- 
portion of  the  live  and  dead  load  equal  to  that  given  by  the  formula  r  =  r  —0.5,  where 

o 

1  =  length  and  b  —  breadth  of  slab.  The  longitudinal  reinforcement  should  then  be 
proportioned  to  carry  the  remainder  of  the  load. 

In  placing  reinforcement  in  such  slabs  account  may  well  be  taken  of  the  fact  that 
the  bending  moment  is  greater  near  the  center  of  the  slab  than  near  the  edges. 
For  this  purpose  two-thirds  of  the  previously  calculated  moments  may  be 
assumed  as  carried  by  the  center  half  of  the  slab  and  one-third  by  the  outside 
quarters. 

Loads  carried  to  beams  by  slabs  which  are  reinforced  in  two  directions  will  not  be 
uniformly  distributed  to  the  supporting  beams  and  the  distribution  will  depend  on 
the  relative  stiffness  of  the  slab  and  the  supporting  beams.  The  distribution  which 
may  be  expected  ordinarily  is  a  variation  of  the  load  in  the  beam  in  accordance  with 
the  ordinates  of  a  parabola,  having  its  vertex  at  the  middle  of  the  span.  For  any 
given  design,  the  probable  distribution  should  be  ascertained  and  the  moments  in  the 
beam  calculated  accordingly. 

Continuous  Beams  and  Slabs.  When  the  beam  or  slab  is  continuous  over  its 
supports,  reinforcement  should  be  fully  provided  at  points  of  negative  moment,  and 
the  stresses  in  concrete  recommended  in  the  section  on  "Working  Stresses,"  should 
not  be  exceeded.  In  computing  the  positive  and  negative  moments  in  beams  and  slabs 
continuous  over  several  supports,  due  to  uniformly  distributed  loads,  the  following 
rules  are  recommended: 

(a)   For  floor  slabs  the  bending  moments  at  center  and  at  support  should  be  taken 

at-pr-  for  both  dead  and  live  loads,  where  w  represents  the  load  per  linear  unit  and  I 
the  span  length. 

(6)  For  beams  the  bending  moment  at  center  and  at  support  for  interior  spans 

wl2,  w  I2 

should  be  taken  at  -y^  and  for  end  spans  it  should  be  taken  at  -y^r    for  center  and 

interior  support,  for  both  dead  and  live  loads. 

(c)  In  the  case  of  beams  and  slabs  continuous  for  two  spans  only,  with  their  ends 
restrained,  the  bending  moment  both  at  the  central  support  and  near  the  middle  of 

wl2 
the  span  should  be  taken  at  —  • 

(d)  At  the  ends  of  continuous  beams  the  amount  of  negative  moment  which  will  be 
developed  in  the  beam  will  depend  on  the  condition  of  restraint  or  fixedness,  and  this 
will  depend  on  the  form  of  construction  used.    In  the  ordinary  cases  a  moment  of 

196 


USEFUL      DATA 

—  may  be  taken;  for  small  beams  running  into  heavy  columns  this  should  be  increased, 

wt2 
but  not  to  exceed  — ^ 

iZi 

For  spans  of  unusual  length,  or  for  spans  of  materially  unequal  length,  more  exact 
calculations  should  be  made.  Special  consideration  is  also  required  in  the  case  of  con- 
centrated loads. 

Even  if  the  center  of  the  span  is  designed  for  a  greater  bending  moment  than  is 
called  for  by  (a)  or  (6),  the  negative  moment  at  the  support  should  not  be  taken  as 
less  than  the  values  there  given. 

Where  beams  are  reinforced  on  the  compression  side,  the  steel  may  be  assumed  to 
carry  its  proportion  of  stress  in  accordance  with  the  ratio  of  moduli  of  elasticity,  as 
given  in  the  section  on  "Working  Stresses."  Reinforcing  bars  for  compression  in  beams 
should  be  straight  and  should  be  two  diameters  in  the  clear  from  the  surface  of  the 
concrete.  For  the  positive  bending  moment,  such  reinforcement  should  not  exceed 
one  per  cent  of  the  area  of  the  concrete.  In  the  case  of  cantilever  and  continuous 
beams,  tensile  and  compressive  reinforcement  over  supports  should  extend  sufficiently 
beyond  the  support  and  beyond  the  point  of  inflection  to  develop  the  requisite  bond 
strength. 

In  construction  made  continuous  over  supports  it  is  important  that  ample  founda- 
tions should  be  provided;  for  unequal  settlements  are  liable  to  produce  unsightly,  if 
not  dangerous  cracks.  This  effect  is  more  likely  to  occur  in  low  structures. 

Girders,  such  as  wall  girders,  which  have  beams  framed  into  one  side  only,  should 
be  designed  to  resist  torsional  moment  arising  from  the  negative  moment  at  the  end 
of  the  beam. 

Bond  Strength  and  Spacing  of  Reinforcement.  Adequate  bond  strength 
should  be  provided.  The  formula  hereinafter  given  for  bond  stresses  in  beams  is  for 
straight  longitudinal  bars.  In  beams  in  which  a  portion  of  the  reinforcement  is  bent 
up  near  the  end,  the  bond  stress  at  places,  in  both  the  straight  bars  and  the  bent  bars, 
will  be  considerably  greater  than  for  all  the  bars  straight,  and  the  stress  at  some  point 
may  be  several  times  as  much  as  that  found  by  considering  the  stress  to  be  uniformly 
distributed  along  the  bar.  In  restrained  and  cantilever  beams  full  tensile  stress  exists 
in  the  reinforcing  bars  at  the  point  of  support  and  the  bars  should  be  anchored  in  the 
support  sufficiently  to  develop  this  stress. 

In  case  of  anchorage  of  bars,  an  additional  length  of  bar  should  be  provided  beyond 
that  found  on  the  assumption  of  uniform  bond  stress,  for  the  reason  that  before  the 
bond  resistance  at  the  end  of  the  bar  can  be  developed  the  bar  may  have  begun  to  slip 
at  another  point  and  "running"  resistance  is  less  than  the  resistance  before  slip  begins. 

Where  high  bond  resistance  is  required,  the  deformed  bar  is  a  suitable  means  of 
supplying  the  necessary  strength.  But  it  should  be  recognized  that  even  with  a  de- 
formed bar  initial  slip  occurs  at  early  loads,  and  that  the  ultimate  loads  obtained  in 
the  usual  tests  for  bond  resistance  may  be  misleading.  Adequate  bond  strength 
throughout  the  length  of  a  bar  is  preferable  to  end  anchorage,  but,  as  an  additional 
safeguard,  such  anchorage  may  properly  be  used  in  special  cases.  Anchorage  furnished 
by  short  bends  at  a  right  angle  is  less  effective  than  by  hooks  consisting  of  turns 
through  180  degrees. 

197 


CORRUGATED   BAR   COMPANY,  INC. 


The  lateral  spacing  of  parallel  bars  should  be  not  less  than  three  diameters  from 
center  to  center,  nor  should  the  distance  from  the  side  of  the  beam  to  the  center  of  the 
nearest  bar  be  less  than  two  diameters.  The  clear  spacing  between  two  layers  of  bars 
should  be  not  less  than  one  inch.  The  use  of  more  than  two  layers  is  not  recommended, 
unless  the  layers  are  tied  together  by  adequate  metal  connections,  particularly  at  and 
near  points  where  bars  are  bent  up  or  bent  down.  Where  more  than  one  layer  is  used 
at  least  all  bars  above  the  lower  layer  should  be  bent  up  and  anchored  beyond  the 
edge  of  the  support. 

Diagonal  Tension  and  Shear.  When  a  reinforced  concrete  beam  is  subjected 
to  flexural  action,  diagonal  tensile  stresses  are  set  up.  A  beam  without  web  reinforce- 
ment will  fail  if  these  stresses  exceed  the  tensile  strength  of  the  concrete.  When  web 
reinforcement,  made  up  of  stirrups  or  of  diagonal  bars  secured  to  the  longitudinal 
reinforcement,  or  of  longitudinal  reinforcing  bars  bent  up  at  several  points,  is  used, 
new  conditions  prevail,  but  even  in  this  case  at  the  beginning  of  loading  the  diagonal 
tension  developed  is  taken  principally  by  the  concrete,  the  deformations  which  are 
developed  in  the  concrete  permitting  but  little  stress  to  be  taken  by  the  web  rein- 
forcement. When  the  resistance  of  the  concrete  to  the  diagonal  tension  is  overcome 
at  any  point  in  the  depth  of  the  beam,  greater  stress  is  at  once  set  up  in  the  web  rein- 
forcement. 

For  homogeneous  beams  the  analytical  treatment  of  diagonal  tension  is  not  very 
complex,  the  diagonal  tensile  stress  is  a  function  of  the  horizontal  and  vertical  shear- 
ing stresses  and  of  the  horizontal  tensile  stress  at  the  point  considered,  and  as  the 
intensity  of  these  three  stresses  varies  from  the  neutral  axis  to  the  remotest  fibre,  the 
intensity  of  the  diagonal  tension  will  be  different  at  different  points  in  the  section, 
and  will  change  with  different  proportionate  dimensions  of  length  to  depth  of  beam. 
For  the  composite  structure  of  reinforced  concrete  beams,  an  analysis  of  the  web 
stresses,  and  particularly  of  the  diagonal  tensile  stresses,  is  very  complex;  and  when 
the  variations  due  to  a  change  from  no  horizontal  tensile  stress  in  the  concrete  at 
remotest  fibre  to  the  presence  of  horizontal  tensile  stress  at  some  point  below  the 
neutral  axis  are  considered,  the  problem  becomes  more  complex  and  indefinite.  Under 
these  circumstances,  in  designing  recourse  is  had  to  the  use  of  the  calculated  vertical 
shearing  stress  as  a  means  of  comparing  or  measuring  the  diagonal  tensile  stresses 
developed,  it  being  understood  that  the  vertical  shearing  stress  is  not  the  numerical 
equivalent  of  the  diagonal  tensile  stress,  and  that  there  is  not  even  a  constant  ratio 
between  them.  It  is  here  recommended  that  the  maximum  vertical  shearing 
stress  in  a  section  be  used  as  the  means  of  comparison  of  the  resistance  to  diagonal 
tensile  stress  developed  in  the  concrete  in  beams  not  having  web  reinforce- 
ment. 

Even  after  the  concrete  has  reached  its  limit  of  resistance  to  diagonal  tension,  if 
the  beam  has  web  reinforcement,  conditions  of  beam  action  will  continue  to  prevail, 
at  least  through  the  compression  area,  and  the  web  reinforcement  will  be  called  on  to 
resist  only  a  part  of  the  web  stresses.  From  experiments  with  beams  it  is  concluded 
that  it  is  safe  practice  to  use  only  two-thirds  of  the  external  vertical  shear  in  making 
calculations  of  the  stresses  that  come  on  stirrups,  diagonal  web  pieces,  and  bent-up 
bars,  and  it  is  here  recommended  for  calculations  in  designing  that  two-thirds  of  the 
external  vertical  shear  be  taken  as  producing  stresses  in  web  reinforcement. 

198 


USEFUL      DATA 


It  is  well  established  that  vertical  members  attached  to  or  looped  about  horizontal 
members,  inclined  members  secured  to  horizontal  members  in  such  a  way  as  to  insure 
against  slip,  and  the  bending  of  a  part  of  the  longitudinal  reinforcement  at  an  angle, 
will  increase  the  strength  of  a  beam  against  failure  by  diagonal  tension,  and  that  a  well- 
designed  and  well-distributed  web  reinforcement  may  under  the  best  conditions 
increase  the  total  vertical  shear  carried  to  a  value  as  much  as  three  times  that  obtained 
when  the  bars  are  all  horizontal  and  no  web  reinforcement  is  used. 

When  web  reinforcement  comes  into  action  as  the  principal  tension  web  resistance, 
the  bond  stresses  between  the  longitudinal  bars  and  the  concrete  are  not  distributed 
as  uniformly  along  the  bars  as  they  otherwise  would  be,  but  tend  to  be  concentrated 
at  and  near  stirrups,  and  at  and  near  the  points  where  bars  are  bent  up.  When  stirrups 
are  not  rigidly  attached  to  the  longitudinal  bars,  and  the  proportioning  of  bars  and 
stirrups  spacing  is  such  that  local  slip  of  bars  occurs  at  stirrups,  the  effectiveness  of 
the  stirrups  is  impaired,  though  the  presence  of  stirrups  still  gives  an  element  of 
toughness  against  diagonal  tension  failure. 

Sufficient  bond  resistance  between  the  concrete  and  the  stirrups  or  diagonals  must 
be  provided  in  the  compression  area  of  the  beam. 

The  longitudinal  spacing  of  vertical  stirrups  should  not  exceed  one-half  the  depth  of 
beam,  and  that  of  inclined  members  should  not  exceed  three-fourths  of  the  depth  of  beam. 

Bending  of  longitudinal  reinforcing  bars  at  an  angle  across  the  web  of  the  beam 
may  be  considered  as  adding  to  diagonal  tension  resistance  for  a  horizontal  distance 
from  the  point  of  bending  equal  to  three-fourths  of  the  depth  of  beam.  Where  the 
bending  is  made  at  two  or  more  points,  the  distance  between  points  of  bending  should 
not  exceed  three-fourths  of  the  depth  of  the  beam.  In  the  case  of  a  restrained  beam 
the  effect  of  bending  up  a  bar  at  the  bottom  of  the  beam  in  resisting  diagonal  tension 
may  not  be  taken  as  extending  beyond  a  section  at  the  point  of  inflection,  and  the 
effect  of  bending  down  a  bar  in  the  region  of  negative  moment  may  be  taken  as  extend- 
ing from  the  point  of  bending  down  of  bar  nearest  the  support  to  a  section  not  more 
than  three-fourths  of  the  depth  of  beam  beyond  the  point  of  bending  down  of  bar 
farthest  from  the  support  but  not  beyond  the  point  of  inflection.  In  case  stirrups  are 
used  in  the  beam  away  from  the  region  in  which  the  bent  bars  are  condsidered  effective, 
a  stirrup  should  be  placed  not  farther  than  a  distance  equal  to  one-fourth  the  depth 
of  beam  from  the  limiting  sections  defined  above.  In  case  the  web  resistance  required 
through  the  region  of  bent  bars  is  greater  than  that  furnished  by  the  bent  bars,  suffi- 
cient additional  web  reinforcement  in  the  form  of  stirrups  or  attached  diagonals 
should  be  provided.  The  higher  resistance  to  diagonal  tension  stresses  given  by  unit 
frames  having  the  stirrups  and  bent-up  bars  securely  connected  together  both  longi- 
tudinally and  laterally  is  worthy  of  recognition.  It  is  necessary  that  a  limit  be  placed 
on  the  amount  of  shear  which  may  be  allowed  in  a  beam;  for  when  web  reinforcement 
sufficiently  efficient  to  give  very  high  web  resistance  is  used,  at  the  higher  stresses  the 
concrete  in  the  beam  becomes  checked  and  cracked  in  such  a  way  as  to  endanger  its 
durability  as  well  as  its  strength. 

The  section  to  be  taken  as  the  critical  section  in  the  calculation  of  shearing  stresses 
will  generally  be  the  one  having  the  maximum  vertical  shear,  though  experiments 
show  that  the  section  at  which  diagonal  tension  failures  occur  is  not  just  at  a  support 
even  though  the  shear  at  the  latter  point  be  much  greater. 

199 


CORRUGATED      BAR      COMPANY,     INC. 


In  the  case  of  restrained  beams,  the  first  stirrup  or  the  point  of  bending  down  of  bar 
should  be  placed  not  farther  than  one-half  of  the  depth  of  beam  away  from  the  face 
of  the  support. 

It  is  important  that  adequate  bond  strength  or  anchorage  be  provided  to  develop 
fully  the  assumed  strength  of  all  web  reinforcement. 

Low  bond  stresses  in  the  longitudinal  bars  are  helpful  in  giving  resistance  against 
diagonal  tension  failures  and  anchorage  of  longitudinal  bars  at  the  ends  of  the  beams 
or  in  the  supports  is  advantageous. 

It  should  be  noted  that  it  is  on  the  tension  side  of  a  beam  that  diagonal  tension 
develops  in  a  critical  way,  and  that  proper  connection  should  always  be  made  between 
stirrups  or  other  web  reinforcement  and  the  longitudinal  tension  reinforcement, 
whether  the  latter  is  on  the  lower  side  of  the  beam  or  on  its  upper  side.  Where  nega- 
tive moment  exists,  as  is  the  case  near  the  supports  in  a  continuous  beam,  web  rein- 
forcement to  be  effective  must  be  looped  over  or  wrapped  around  or  be  connected  with 
the  longitudinal  tension  reinforcing  bars  at  the  top  of  the  beam  in  the  same  way  as 
is  necessary  at  the  bottom  of  the  beam  at  sections  where  the  bending  moment  is 
positive. 

Inasmuch  as  the  smaller  the  longitudinal  deformations  in  the  horizontal  reinforce- 
ment are,  the  less  the  tendency  for  the  formation  of  diagonal  cracks,  a  beam  will  be 
strengthened  against  diagonal  tension  failure  by  so  arranging  and  proportioning  the 
horizontal  reinforcement  that  the  unit  stresses  at  points  of  large  shear  shall  be  rela- 
tively low. 

It  does  not  seem  feasible  to  make  a  complete  analysis  of  the  action  of  web  rein- 
forcement, and  more  or  less  empirical  methods  of  calculation  are  therefore  employed. 
Limiting  values  of  working  stresses  for  different  types  of  web  reinforcement  are  given 
in  the  section  on  "Working  Stresses."  The  conditions  apply  to  cases  commonly  met 
in  design.  It  is  assumed  that  adequate  bond  resistance  or  anchorage  of  all  web  rein- 
forcement will  be  provided. 

When  a  flat  slab  rests  on  a  column,  or  a  column  bears  on  a  footing,  the  vertical 
shearing  stresses  in  the  slab  or  footing  immediately  adjacent  to  the  column  are  termed 
punching  shearing  stresses.  The  element  of  diagonal  tension,  being  a  function  of  the 
bending  moment  as  well  as  of  shear,  may  be  small  in  such  cases,  or  may  be  otherwise 
provided  for.  For  this  reason  the  permissible  limit  of  stress  for  punching  shear  may  be 
higher  than  the  allowable  limit  when  the  shearing  stress  is  used  as  a  means  of  com- 
paring diagonal  tensile  stress.  The  working  values  recommended  are  given  in  the 
section  on  "Working  Stresses." 

Columns.  By  columns  are  meant  compression  members  of  which  the  ratio  of 
unsupported  length  to  least  width  exceeds  about  four,  and  which  are  provided  with 
reinforcement  of  one  of  the  forms  hereafter  described. 

It  is  recommended  that  the  ratio  of  unsupported  length  of  column  to  its  least  width 
be  limited  to  fifteen. 

The  effective  area  of  hooped  columns  or  columns  reinforced  with  structural  shapes 
shall  be  taken  as  the  area  within  the  circle  enclosing  the  spiral  or  the  polygon  enclos- 
ing the  structrual  shapes. 

Columns  may  be  reinforced  by  longitudinal  bars;  by  bands,  hoops,  or  spirals,  to- 
gether with  longitudinal  bars;  or  by  structural  forms  which  are  sufficiently  rigid  to 

200 


USEFUL      DATA 


have  value  in  themselves  as  columns.  The  general  effect  of  closely  spaced  hooping  is 
to  greatly  increase  the  toughness  of  the  column  and  to  add  to  its  ultimate  strength, 
but  hooping  has  little  effect  on  its  behavior  within  the  limit  of  elasticity.  It  thus 
renders  the  concrete  a  safer  and  more  reliable  material,  and  should  permit  the  use  of 
a  somewhat  higher  working  stress.  The  beneficial  effects  of  toughening  are  adequately 
provided  by  a  moderate  amount  of  hooping,  a  larger  amount  serving  mainly  to  increase 
the  ultimate  strength  and  the  deformation  possible  before  ultimate  failure. 

Composite  columns  of  structural  steel  and  concrete  in  which  the  steel  forms  a  column 
by  itself  should  be  designed  with  caution.  To  classify  this  type  as  a  concrete  column 
reinforced  with  structural  steel  is  hardly  permissible,  as  the  steel,  generally,  will  take 
the  greater  part  of  the  load.  When  this  type  of  column  is  used,  the  concrete  should 
be  adequately  tied  together  by  tie  plates  or  lattice  bars,  which,  together  with  other 
details,  such  as  splices,  etc.,  should  be  designed  in  conformity  with  standard  practice 
for  structural  steel.  The  concrete  may  exert  a  beneficial  effect  in  restraining  the  steel 
from  lateral  deflection  and  also  in  increasing  the  carrying  capacity  of  the  column.  The 
proportion  of  load  to  be  carried  by  the  concrete  will  depend  on  the  form  of  the  column 
and  the  method  of  construction.  Generally,  for  high  percentages  of  steel,  the  concrete 
will  develop  relatively  low  unit  stresses,  and  caution  should  be  used  in  placing  depend- 
ence on  the  concrete, 

The  following  recommendations  are  made  for  the  relative  working  stresses  in  the 
concrete  for  the  several  types  of  columns : 

(a)  Columns  with  longitudinal  reinforcement  to  the  extent  of  not  less  than  1  per 
cent  and  not  more  than  4  per  cent,  and  with  lateral  ties  of  not  less  than  %  inch  in 
diameter  12  inches  apart,  nor  more  than  16  diameters  of  the  longitudinal  bar:  the 
unit  stress  recommended  for  axial  compression,  on  concrete  piers  having  a  length  not 
more  than  four  diameters,  in  section  on  "Working  Stresses." 

(6)  Columns  reinforced  with  not  less  than  1  per  cent  and  not  more  than  4  per  cent 
of  longitudinal  bars  and  with  circular  hoops  or  spirals  not  less  than  1  per  cent  of  the 
volume  of  the  concrete  and  as  hereinafter  specified:  a  unit  stress  55  per  cent  higher 
than  given  for  (a),  provided  the  ratio  of  unsupported  length  of  column  to  diameter  of 
the  hooped  core  is  not  more  than  10. 

The  foregoing  recommendations  are  based  on  the  following  conditions: 

It  is  recommended  that  the  minimum  size  of  columns  to  which  the  working  stresses 
may  be  applied  be  12  inches  out  to  out. 

In  all  cases  longitudinal  reinforcement  is  assumed  to  carry  its  proportion  of  stress 
in  accordance  with  Section  (c)  6,  page  195.  The  hoops  or  bands  are  not  to  be  counted 
on  directly  as  adding  to  the  strength  of  the  column. 

Longitudinal  reinforcement  bars  should  be  maintained  straight,  and  should 
have  sufficient  lateral  support  to  be  securely  held  in  place  until  the  concrete 
has  set. 

Where  hooping  is  used,  the  total  amount  of  such  reinforcement  shall  be  not  less  than 
one  per  cent  of  the  volume  of  the  column,  enclosed.  The  clear  spacing  of  such  hooping 
shall  not  be  greater  than  one-sixth  the  diameter  of  the  enclosed  column  and  preferably 
not  greater  than  one-tenth,  and  in  no  case  more  than  2^in.  Hooping  is  to  be  circular 
and  the  ends  of  bands  must  be  united  in  such  a  way  as  to  develop  their  full  strength. 
Adequate  means  must  be  provided  to  hold  bands  or  hoops  in  place  so  as  to  form  a 

201 


CORRUGATED   BAR   COMPANY,  INC. 


column,  the  core  of  which  shall  be  straight  and  well  centered.  The  strength  of  hooped 
columns  depends  very  much  upon  the  ratio  of  length  to  diameter  of  hooped  core,  and 
the  strength  due  to  hooping  decreases-  rapidly  as  this  ratio  increases  beyond  five. 
The  working  stresses  recommended  are  for  hooped  columns  with  a  length  of  not  more 
than  ten  diameters  of  the  hooped  core. 

The  Committee  has  no  recommendation  to  make  for  a  formula  for  working  stresses 
for  columns  longer  than  ten  diameters. 

Bending  stresses  due  to  eccentric  loads,  such  as  unequal  spans  of  beams,  and  to  lateral 
forces,  must  be  provided  for  by  increasing  the  section  until  the  maximum  stress  does 
not  exceed  the  values  above  specified.  Where  tension  is  possible  in  the  longitudinal 
bars  of  the  columns,  adequate  connection  between  the  ends  of  the  bars  must  be  pro- 
vided to  take  this  tension. 

Reinforcing  for  Shrinkage  and  Temperature  Stresses.  When  areas  of  con- 
crete too  large  to  expand  and  contract  freely  as  a  whole  are  exposed  to  atmospheric 
conditions,  the  changes  of  form  due  to  shrinkage  and  to  action  of  temperature  are 
such  that  cracks  may  occur  in  the  mass  unless  precautions  are  taken  to  distribute  the 
stresses  so  as  to  prevent  the  cracks  altogether  or  to  render  them  very  small.  The  dis- 
tance apart  of  the  cracks,  and  consequently  their  size,  will  be  directly  proportional  to 
the  diameter  of  the  reinforcement  and  to  the  tensile  strength  of  the  concrete,  and 
inversely  proportional  to  the  percentage  of  reinforcement  and  also  to  its  bond  resis- 
tance per  unit  of  surface  area.  To  be  most  effective,  therefore,  reinforcement  (in  amount 
generally  not  less  than  one-third  of  one  per  cent  of  the  gross  area)  of  a  form  which 
will  develop  a  high  bond  resistance  should  be  placed  near  the  exposed  surface  and  be 
well  distributed.  Where  openings  occur  the  area  of  cross-section  of  the  reinforcement 
should  not  be  reduced.  The  allowable  size  and  spacing  of  cracks  depends  on  various 
considerations,  such  as  the  necessity  for  water-tightness,  the  importance  of  appearance 
of  the  surface,  and  the  atmospheric  changes. 

The  tendency  of  concrete  to  shrink  makes  it  necessary,  except  where  expansion  is 
provided  for,  to  thoroughly  connect  the  component  parts  of  the  frame  of  articulated 
structures,  such  as  floor  and  wall  members  in  buildings,  by  the  use  of  suitable  rein- 
forcing material.  The  amount  of  reinforcement  for  such  connection  should  bear  some 
relation  to  the  size  of  the  members  connected,  larger  and  heavier  members  requiring 
stronger  connections.  The  reinforcing  bars  should  be  extended  beyond  the  critical 
section  far  enough,  or  should  be  sufficiently  anchored  to  develop  their  full  tensile 
strength. 

Flat  Slab.  The  continuous  flat  slab  reinforced  in  two  or  more  directions  and 
built  monolithically  with  the  supporting  columns  (without  beams  or  girders)  is  a 
type  of  construction  which  is  now  extensively  used  and  which  has  recognized  advan- 
tages for  certain  types  of  structures  as,  for  example,  warehouses  in  which  large,  open 
floor  space  is  desired.  In  its  construction,  there  is  excellent  opportunity  for  inspecting 
the  position  of  the  reinforcement.  The  conditions  attending  deposition  and  placing 
of  concrete  are  favorable  to  securing  uniformity  and  soundness  in  the  concrete.  The 
recommendations  in  the  following  paragraphs  relate  to  flat  slabs  extending  over 
several  rows  of  panels  in  each  direction.  Necessarily  the  treatment  is  more  or  less 
empirical. 

The  co-efficients  and  moments  given  relate  to  uniformly  distributed  loads. 


USEFUL      DATA 


(a)  Column  Capital. — It  is  usual  in  flat  slab  construction  to  enlarge  the  supporting 
columns  at  their  top,  thus  forming  column  capitals.  The  size  and  shape  of  the  column 
capital  affect  the  strength  of  the  structure  in  several  ways.  The  moment  of  the  external 
forces  which  the  slab  is  called  upon  to  resist  is  dependent  upon  the  size  of  the  capital; 
the  section  of  the  slab  immediately  above  the  upper  periphery  of  the  capital  carries 
the  highest  amount  of  punching  shear;  and  the  bending  moment  developed  in  the 
column  by  an  eccentric  or  unbalanced  loading  of  the  slab  is  greatest  at  the  under 
surface  of  the  slab.  Generally  the  horizontal  section  of  the  column  capital  should  be 
round  or  square  with  rounded  corners.  In  oblong  panels  the  section  may  be  oval  or 
oblong,  with  dimensions  proportional  to  the  panel  dimensions.  For  computation 
purposes,  the  diameter  of  the  column  capital  will  be  considered  to  be  measured  where 
its  vertical  thickness  is  at  least  1%  inches,  provided  the  slope  of  the  capital  below 
this  point  nowhere  makes  an  angle  with  the  vertical  of  more  than  45  degrees.  In  case 
a  cap  is  placed  above  the  column  capital,  the  part  of  this  cap  within  a  cone  made  by 
extending  the  lines  of  the  column  capital  upward  at  the  slope  of  45  degrees  to  the  bot- 
tom of  the  slab  or  dropped  panel  may  be  considered  as  part  of  the  column  capital  in 
determining  the  diameter  for  design  purposes.  Without  attempting  to  limit  the  size 
of  the  column  capital  for  special  cases,  it  is  recommended  that  the  diameter  of  the 
column  capital  (or  its  dimension  parallel  to  the  edge  of  the  panel)  generally  be  made 
not  less  than  one-fifth  of  the  dimension  of  the  panel  from  center  to  center  of  adjacent 
columns.  A  diameter  equal  to  0.225  of  the  panel  length  has  been  used  quite  widely 
and  acceptably.  For  heavy  loads  or  large  panels  especial  attention  should  be  given  to 
designing  and  reinforcing  the  column  capital  with  respect  to  compressive  stresses  and 
bending  moments.  In  the  case  of  heavy  loads  or  large  panels,  and  where  the  condi- 
tions of  the  panel  loading  or  variations  in  panel  length  or  other  conditions  cause  high 
bending  stresses  in  the  column,  and  also  for  column  capitals  smaller  than  the  size 
herein  recommended,  especial  attention  should  be  given  to  designing  and  reinforcing 
the  column  capital  with  respect  to  compression  and  to  rigidity  of  connection  to  floor 
slab. 

(6)  Dropped  Panel, — In  one  type  of  construction  the  slab  is  thickened  throughout 
an  area  surrounding  the  column  capital.  The  square  or  oblong  of  thickened  slab  thus 
formed  is  called  a  dropped  panel  or  a  drop.  The  thickness  and  the  width  of  the  dropped 
panel  may  be  governed  by  the  amount  of  resisting  moment  to  be  provided  (the  com- 
pressive stress  in  the  concrete  being  dependent  upon  both  thickness  and  width),  or 
its  thickness  may  be  governed  by  the  resistance  to  shear  required  at  the  edge  of  the 
column  capital  and  its  width  by  the  allowable  compressive  stresses  and  shearing 
stresses  in  the  thinner  portion  of  the  slab  adjacent  to  the  dropped  panel.  Generally 
however,  it  is  recommended  that  the  width  of  the  dropped  panel  be  at  least  four- 
tenths  of  the  corresponding  side  of  the  panel  as  measured  from  center  to  center  of 
columns,  and  that  the  offset  in  thickness  be  not  more  than  five-tenths  of  the  thickness 
of  the  slab  outside  the  dropped  panel. 

(c)  Slab  Thickness. — In  the  design  of  a  slab,  the  resistance  to  bending  and  to  shear- 
ing forces  will  largely  govern  the  thickness,  and,  in  the  case  of  large  panels  with  light 
loads,  resistance  to  deflection  may  be  a  controlling  factor.  The  following  formulas 
for  minimum  thicknesses  are  recommended  as  general  rules  of  design  when  the  diameter 
of  the  column  capital  is  not  less  than  one-fifth  of  the  dimension  of  the  panel  from 

203 


CORRUGATED      BAR      COMPANY,     INC. 


center  to  center  of  adjacent  columns,  the  large  dimension  being  used  in  the  case  of 
oblong  panels.    For  notation,  let 

t  —  Total  thickness  of  slab  in  inches. 
L  =  Panel  length  in  feet. 

«0=Sum  of  live  load  and  dead  load  in  pounds  per  square  foot. 
Then,    for   a    slab    without    dropped    panels,    minimum    t=Q.Q24L\/w+l% 
for    a    slab    with    dropped    panels,    minimum    t=Q.Q2L\/rw-}-l;   for    a    dropped 
panel    whose    width    is    four-tenths    of    the    panel    length,      minimum 


<=0.03 


In  no  case  should  the  slab  thickness  be  made  less  than  six  inches,  nor 
should  the  thickness  of  a  floor  slab  be  made  less  than  one-thirty-second  of 
the  panel  length,  nor  the  thickness  of  a  roof  slab  less  than  one-fortieth  of  the 
panel  length. 

(d)  Bending  and  Resisting  Moments  in  Slabs.  —  If  a  vertical  section  of  a  slab  be  taken 
across  a  panel  along  a  line  midway  between  columns,  and  if  another  section  be  taken 


rf 


Column-Head 
Section 


Mid-Section 


Column-Head 


Position  of  resultant 
of  shear  on  quarter 
peripheries  of  two 
column  capitals. 


Center  of  Gravity 
of  load  on  half 
panel. 


tion 


Outer 
Section 


Inner 
Secti°n 


!*—  \l--~  -*  ....... 


\l 


Outer 


FIG.  10 


FIG.  11 


along  an  edge  of  the  panel  parallel  to  the  first  section,  but  skirting  the  part  of  the 
periphery  of  the  column  capitals  at  the  two  corners  of  the  panels,  the  moment  of  the 
couple  formed  by  the  external  load  on  the  half  panel,  exclusive  of  that  over  the  column 
capital  (sum  of  dead  and  live  load)  and  the  resultant  of  the  external  shear  or  reaction  at 
the  support  at  the  two  column  capitals  (see  Fig.  10),  may  be  found  by  ordinary  static 
analysis.  It  will  be  noted  that  the  edges  of  the  area  here  considered  are  along  lines  of 
zero  shear  except  around  the  column  capitals.  This  moment  of  the  external  forces 
acting  on  the  half  panel  will  be  resisted  by  the  numerical  sum  of  (a)  the  moment  of 
the  internal  stresses  at  the  section  of  the  panel  midway  between  columns  (positive 
resisting  moment)  and  (6)  the  moment  of  the  internal  stresses  at  the  section  referred 
to  at  the  end  of  the  panel  (negative  resisting  moment).  In  the  curved  portion  of  the 
end  section  (that  skirting  ihe  column),  the  stresses  considered  are  the  components 
which  act  parallel  to  the  normal  stresses  on  the  straight  portion  of  the  section.  An- 
alysis shows  that,  for  a  uniformly  distributed  load,  and  round  columns,  and  square 


204 


USEFUL      DATA 


panels,  the  numerical  sum  of  the  positive  moment  and  the  negative  moment  at  the 
two  sections  named  is  given  quite  closely  by  the  equation 


In  this  formula  and  in  those  which  follow  relating  to  oblong  panels: 

w  =sum  of  the  live  and  dead  load  per  unit  of  area; 

I    =side  of  a  square  panel  measured  from  center  to  center  of  columns; 

l\  =one  side  of  the  oblong  panel  measured  from  center  to  center  of  columns; 

/2  =  other  side  of  oblong  panel  measured  in  the  same  way; 

c   =  diameter  of  the  column  capital; 

Mx  =  numerical  sum  of  positive  moment  and  negative  moment  in  one  direction. 
My  =  numerical  sum  of  positive  moment  and  negative  moment  in  the  other  direction. 

(See  paper  and  closure,  Statical  Limitations  upon  the  Steel  Requirement  in  Rein- 
forced Concrete  Flat  Slab  Floors,  by  John  R.  Nichols,  Jun.  Am.  Soc.  C.  E.,  Transac- 
tions Am.  Soc.  C.  E.  Vol.  LXXVII.) 

For  oblong  panels,  the  equations  for  the  numerical  sums  of  the  positive  moment 
and  the  negative  moment  at  the  two  sections  named  become, 


Where  Afx  =  is  the  numerical  sum  of  the  positive  moment  and  the  negative  moment 
for  the  sections  parallel  to  the  dimensions  lz,  and  My  is  the  numerical  sum  of  the 
positive  moment  and  the  negative  moment  for  the  sections  parallel  to  the 
dimensions  l\. 

What  proportion  of  the  total  resistance  exists  as  positive  moment  and  what  as 
negative  moment  is  not  readily  determined.  The  amount  of  the  positive  moment 
and  that  of  the  negative  moment  may  be  expected  to  vary  somewhat  with  the  design 
of  the  slab.  It  seems  proper,  however,  to  make  the  division  of  total  resisting  moment 
in  the  ratio  of  three-eighths  for  the  positive  moment  to  five-eighths  for  the  negative 
moment. 

With  reference  to  variations  in  stress  along  the  sections,  it  is  evident  from  condi- 
tions of  flexure  that  the  resisting  moment  is  not  distributed  uniformly  along  either 
the  section  of  positive  moment  or  that  of  negative  moment.  As  the  law  of  the  distri- 
bution is  not  known  definitely,  it  will  be  necessary  to  make  an  empirical  apportion- 
ment along  the  sections;  and  it  will  be  considered  sufficiently  accurate  generally  to 
divide  the  sections  into  two  parts  and  to  use  an  average  value  over  each  part  of  the 
panel  section. 

The  relatively  large  breadth  of  structure  in  a  flat  slab  makes  the  effect  of  local 
variations  in  the  concrete  less  than  would  be  the  case  for  narrow  members  like  beams. 
The  tensile  resistance  of  the  concrete  is  less  affected  by  cracks.  Measurements  of 
deformations  in  buildings  under  heavy  load  indicate  the  presence  of  considerable 
tensile  resistance  in  the  concrete,  and  the  presence  of  this  tensile  resistance  acts  to 
decrease  the  intensity  of  the  compressive  stresses.  It  is  believed  that  the  use  of  moment 
co-efficients  somewhat  less  than  those  given  in  a  preceding  paragraph  as  derived  by 
analysis  is  warranted,  the  calculations  of  resisting  moment  and  stresses  in  concrete 

205 


CORRUGATED   BAR   COMPANY,  INC. 


and  reinforcement  being  made  according  to  the  assumptions  specified  m  this  report 
and  no  change  being  made  in  the  values  of  the  working  stresses  ordinarily  used.  Ac- 
cordingly, the  values  of  the  moments  which  are  recommended  for  use  are  somewhat 
less  than  those  derived  by  analysis.  The  values  given  may  be  used  when  the  column 
capitals  are  round,  oval,  square  or  oblong. 

(e)  Names  for  Moment  Sections. — For  convenience,  that  portion  of  the  section 
across  a  panel  along  a  line  midway  between  columns  which  lies  within  the  middle  two 
quarters  of  the  width  of  the  panel  (HI,  Fig.  11),  will  be  called  the  inner  section,  and 
that  portion  in  the  two  outer  quarters  of  the  width  of  the  panel  (GH  and  IJ,  Fig.  11) 
will  be  called  the  outer  sections.  Of  the  section  which  follows  a  panel  edge  from  column 
capital  to  column  capital  and  which  includes  the  quarter  peripheries  of  the  edges  of 
two  column  capitals,  that  portion  within  the  middle  two  quarters  of  the  panel  width 
(CD,  Fig.  11)  will  be  called  the  mid-section,  and  the  two  remaining  portions  (ABC 
and  DEF,  Fig.  11),  each  having  a  projected  width  equal  to  one-fourth  of  the  panel 
width,  will  be  called  the  column-head  sections. 

(/)  Positive  Moment. — For  a  square  interior  panel,  it  is  recommended  that  the  posi- 
tive moment  for  a  section  in  the  middle  of  a  panel  extending  across  its  width  be  taken 

as  —  wl  1 1—  TT-  I  •   Of  this  moment,  at  least  25  per  cent  should  be  provided  for  in  the 

inner  section;  in  the  two  outer  sections  of  the  panel  at  least  55  per  cent  of  the  specified 
moment  should  be  provided  for  in  slabs  not  having  dropped  panels,  and  at  least  60 
jer  cent  in  slabs  having  dropped  panels,  except  that  in  calculations  to  determine 
necessary  thickness  of  slab  away  from  the  dropped  panel  at  least  70  per  cent 
of  the  positive  moment  should  be  considered  as  acting  in  the  two  outer 
sections. 

(g)  Negative  Moment. — For  a  square  interior  panel,  it  is  recommended  that  the 
negative  moment  for  a  section  which  follows  a  panel  edge  from  column  capital  to 
column  capital  and  which  includes  the  quarter  peripheries  of  the  edges  of  the  two 
column  capitals  (the  section  altogether  forming  the  projected  width  of  the  panel)  be 

taken  as  —  w>Z  IZ— —  I   .    Of  this  negative  moment,  at  least  20  per  cent  should  be 

provided  for  in  the  mid-section  and  at  least  65  per  cent  in  the  two  column-head  sec- 
tions of  the  panel,  except  that  in  slabs  having  dropped  panels  at  least  80  per  cent  of 
the  specified  negative  moment  should  be  provided  for  in  the  two  column-head  sections 
of  the  panel. 

(h)  Moments  for  Oblong  Panels. — When  the  length  of  a  panel  does  not  exceed  the 
breadth  by  more  than  5  per  cent,  computation  may  be  made  on  the  basis  of  a  square 
panel  with  sides  equal  to  the  mean  of  the  length  and  the  breadth. 

When  the  long  side  of  an  interior  oblong  panel  exceeds  the  short  side  by  more  than 
one-twentieth  and  by  not  more  than  one-third  of  the  short  side,  it  is  recommended  that 

the  positive  moment  be  taken  as ^zwlz  1 l\—  77- 1    on  a  section  parallel  to  the  dimension 

1        /       2c\ 2 
/2,  and—  wlAh—  =- 1     on  a  section  parallel  to  dimension  ZT;  and  that  the  negative 

1        /       2c\ 2 
moment  be  taken  as  r-=  wlz  I  h — r- 1      on  a  section  at  the  edge  of  the  panel  correspond- 

206 


USEFUL      DATA 


ing  to  the  dimension  Z2,  and  rrzwli  I  k  — «^  1      at  a  section  in  the  other  direction.    The 

limitations  of  the  apportionment  of  moment  between  inner  section  and  outer  section 
and  between  mid-section  and  column-head  sections  may  be  the  same  as  for  square 
panels. 

(i)  Wall  Panels. — The  co-efficient  of  negative  moment  at  the  first  row  of  columns 
away  from  the  wall  should  be  increased  20  per  cent  over  that  required  for  interior 
panels,  and  likewise  the  co-efficient  of  positive  moment  at  the  section  hah*  way  to  the 
wall  should  be  increased  by  20  per  cent.  If  girders  are  not  provided  along  the  wall 
or  the  slab  does  not  project  as  a  cantilever  beyond  the  column  line,  the  reinforcement 
parallel  to  the  wall  for  the  negative  moment  in  the  column-head  section  and  for  the 
positive  moment  in  the  outer  section  should  be  increased  by  20  per  cent.  If  the  wall 
is  carried  by  the  slab  this  concentrated  load  should  be  provided  for  in  the  design  of 
the  slab.  The  co-efficient  of  negative  moments  at  the  wall  to  take  bending  in  the 
direction  perpendicular  to  the  wall  line  may  be  determined  by  the  conditions  of  re- 
straint and  fixedness  as  found  from  the  relative  stiffness  of  columns  and  slab,  but  in 
no  case  should  it  be  taken  as  less  than  one-half  of  that  for  interior  panels. 

(j)  Reinforcement — In  the  calculation  of  moments  all  the  reinforcing  bars  which 
cross  the  section  under  consideration  and  which  fulfill  the  requirements  given  under 
paragraph  (/)  of  this  chapter  may  be  used.  For  a  column-head  section  reinforcing 
bars  parallel  to  the  straight  portion  of  the  section  do  not  contribute  to  the  negative 
resisting  moment  for  the  column-head  section  in  question.  In  the  case  of  four-way 
reinforcement  the  sectional  area  of  the  diagonal  bars  multiplied  by  the  sine  of  the 
angle  between  the  diagonal  of  the  panel  and  straight  portion  of  the  section  under 
consideration  may  be  taken  to  act  as  reinforcement  in  a  rectangular  direction. 

(k)  Point  of  Inflection. — For  the  purpose  of  making  calculations  of  moments  at 
sections  away  from  the  sections  of  negative  moment  and  positive  moment  already 
specified,  the  point  of  inflection  on  any  line  parallel  to  a  panel  edge  may  be  taken  as 
one-fifth  of  the  clear  distance  on  that  line  between  the  two  sections  of  negative  moment 
at  the  opposite  ends  of  the  panel  indicated  in  paragraph  (e),  of  this  chapter.  For  slabs 
having  dropped  panels  the  co-efficient  of  one-fourth  should  be  used  instead  of  one-fifth. 

(t)  Arrangement  of  Reinforcement. — The  design  should  include  adequate  provision 
for  securing  the  reinforcement  in  place  so  as  to  take  not  only  the  maximum  moments, 
but  the  moments  at  intermediate  sections.  All  bars  in  rectangular  bands  or  diagonal 
bands  should  extend  on  each  side  of  a  section  of  maximum  moment,  either  positive 
or  negative,  to  points  at  least  twenty  diameters  beyond  the  point  of  inflection  as  defined 
herein  or  be  hooked  or  anchored  at  the  point  of  inflection.  In  addition  to  this  provision 
bars  in  diagonal  bands  used  as  reinforcement  for  negative  moment  should  extend  on 
each  side  of  a  line  drawn  through  the  column  center  at  right  angles  to  the  direction  of 
the  band  at  least  a  distance  equal  to  thirty-five  one-hundredths  of  the  panel  length, 
and  bars  in  diagonal  bands  used  as  reinforcement  for  positive  moment  should  extend 
on  each  side  of  a  diagonal  through  the  center  of  the  panel  at  least  a  distance  equal  to 
thirty-five  one-hundredths  of  the  panel  length;  and  no  splice  by  lapping  should  be 
permitted  at  or  near  regions  of  maximum  stress  except  as  just  described.  Continuity 
of  reinforcing  bars  is  considered  to  have  advantages,  and  it  is  recommended  that  not 
more  than  one-third  of  the  reinforcing  bars  in  any  direction  be  made  of  a  length  less 

207 


CORRUGATED   BAR   COMPANY,  INC. 


than  the  distance  center  to  center  of  columns  in  that  direction.  Continuous  bars 
should  not  all  be  bent  up  at  the  same  point  of  their  length,  but  the  zone  in  which  this 
bending  occurs  should  extend  on  each  side  of  the  assumed  point  of  inflection,  and 
should  cover  a  width  of  at  least  one-fifteenth  of  the  panel  length.  Mere  draping  of  the 
bars  should  not  be  permitted.  In  four-way  reinforcement  the  position  of  the  bars  in 
both  diagonal  and  rectangular  directions  may  be  considered  in  determining  whether 
the  width  of  zone  of  bending  is  sufficient. 

(m)  Reinforcement  at  Construction  Joints. — It  is  recommended  that  at  construction 
joints  extra  reinforcing  bars  equal  in  section  to  20  per  cent  of  the  amount  necessary 
to  meet  the  requirements  for  moments  at  the  section  where  the  joint  is  made  be  added 
to  the  reinforcement,  these  bars  to  extend  not  less  than  50  diameters  beyond  the  joint 
on  each  side. 

(n)  Tensile  and  Compressive  Stresses. — The  usual  method  of  calculating  the  tensile 
and  compressive  stresses  in  the  concrete  and  in  the  reinforcement,  based  on  the  assump- 
tions for  internal  stresses  given  in  this  chapter,  should  be  followed.  In  the  case  of  the 
dropped  panel  the  section  of  the  slab  and  dropped  panel  may  be  considered  to  act 
integrally  for  a  width  equal  to  the  width  of  the  column-head  section. 

(o)  Provision  for  Diagonal  Tension  and  Shear. — In  calculations  for  the  shearing 
stress  which  is  to  be  used  as  the  means  of  measuring  the  resistance  to  diagonal  tension 
stress,  it  is  recommended  that  the  total  vertical  shear  on  two  column-head  sections 
constituting  a  width  equal  to  one-half  the  lateral  dimensions  of  the  panel,  for  use  in 
the  formula  for  determining  critical  shearing  stresses,  be  considered  to  be  one-fourth 
of  the  total  dead  and  live  load  on  a  panel  for  a  slab  of  uniform  thickness,  and  to  be 
three-tenths  of  the  sum  of  the  dead  and  live  loads  on  a  panel  for  a  slab  with  dropped 

panels.    The  formula  for  shearing  unit  stress  may  then  be  written  v==     ,  . , —  for  slabs 

of  uniform  thickness,  and  v=     '      —  for  slabs  with  dropped  panels,  where  W  is  the 

sum  of  the  dead  and  live  load  on  a  panel,  b  is  half  the  lateral  dimension  of  the  panel 
measured  from  center  to  center  of  columns,  and  jd  is  the  lever  arm  of  the  resisting 
couple  at  the  section. 

The  calculation  of  what  is  commonly  called  punching  shear  may  be  made  on  the 
assumption  of  a  uniform  distribution  over  the  section  of  the  slab  around  the  peri- 
phery of  the  column  capital  and  also  of  a  uniform  distribution  over  the  section  of  the 
slab  around  the  periphery  of  the  dropped  panel,  using  in  each  case  an  amount  of 
vertical  shear  greater  by  25  per  cent  than  the  total  vertical  shear  on  the  section  under 
consideration. 

The  values  of  working  stresses  should  be  those  recommended  for  diagonal  tension 
and  shear  in  the  section  on  "Working  Stresses." 

(p)  Walls  and  Openings. — Girders  or  beams  should  be  constructed  to  carry  walls 
and  other  concentrated  loads  which  are  in  excess  of  the  working  capacity  of  the  slab. 
Beams  should  also  be  provided  in  case  openings  in  the  floor  reduce  the  working  strength 
of  the  slab  below  the  required  carrying  capacity. 

(q)  Unusual  Panels. — The  co-efficients,  apportionments,  and  thicknesses  recom- 
mended are  for  slabs  which  have  several  rows  of  panels  in  each  direction,  and  in  which 
the  size  of  the  panels  is  approximately  the  same.  For  structures  having  a  width  of  one, 

208 


USEFUL      DATA 


two,  or  three  panels,  and  also  for  slabs  having  panels  of  markedly  different  sizes,  an 
analysis  should  be  made  of  the  moments  developed  in  both  slab  and  columns,  and  the 
values  given  herein  modified  accordingly.  Slabs  with  paneled  ceiling  or  with  depressed 
paneling  in  the  floor  are  to  be  considered  as  coming  under  the  recommendations 
herein  given. 

(r)  Bending  Moments  in  Columns. — Provision  should  be  made  in  both  wall  columns 
and  interior  columns  for  the  bending  moment  which  will  be  developed  by  unequally 
loaded  panels,  eccentric  loading,  or  uneven  spacing  of  columns.  The  amount  of  mo- 
ment to  be  taken  by  a  column  will  depend  upon  the  relative  stiffness  of  columns  and 
slab,  and  computations  may  be  made  by  rational  methods,  such  as  the  principal  of 
least  work,  or  of  slope  and  deflection.  Generally,  the  larger  part  of  the  unequalized 
negative  moment  will  be  transmitted  to  the  columns,  and  the  column  should  be 
designed  to  resist  this  bending  moment.  Especial  attention  should  be  given  to  wall 
columns  and  corner  columns. 

WORKING  STRESSES 

General  Assumptions.  The  following  working  stresses  are  recommended  for 
static  loads.  Proper  allowances  for  vibration  and  impact  are  to  be  added  to  live 
loads  where  necessary  to  produce  an  equivalent  static  load  before  applying  the  unit 
stresses  in  proportioning  parts. 

In  selecting  the  permissible  working  stress  on  concrete,  the  designer  should  be 
guided  by  the  working  stresses  usually  allowed  for  other  materials  of  construction, 
so  that  all  structures  of  the  same  class  composed  of  different  materials  may  have 
approximately  the  same  degree  of  safety. 

The  following  recommendations  as  to  allowable  stresses  are  given  in  the  form  of 
percentages  of  the  ultimate  strength  of  the  particular  concrete  which  is  to  be  used; 
this  ultimate  strength  is  that  developed  at  an  age  of  twenty-eight  days,  in  cylinders  8 
inches  in  diameter  and  16  inches  long,  of  proper  consistency f  made  and  stored  under 
laboratory  conditions.  In  the  absence  of  definite  knowledge  in  advance  of  construc- 
tion as  to  just  what  strength  may  be  expected,  the  committee  submits  the  following 
values  as  those  which  should  be  obtained  with  materials  and  workmanship  in  accord- 
ance with  the  recommendations  of  this  report. 

Although  occasional  tests  may  show  higher  results  than  those  here  given,  the  Com- 
mittee recommends  that  these  values  should  be  the  maximum  used  in  design. 

TABLE  OF  COMPRESSIVE  STRENGTHS  OF  DIFFERENT  MIXTURES  OF  CONCRETE 
(In  Pounds  per  Square  Inch) 


Aggregate 

1:3* 

1:4H* 

1:6* 

1:7H* 

1:9* 

Granite,  trap  rock      

3300 

2800 

2200 

1800 

1400 

Gravel,  hard  limestone  and  hard  sandstone  .    .    . 

3000 

2500 

2000 

1600 

1300 

Soft  limestone  and  sandstone                          .    . 

2200 

1800 

1500 

1200 

1000 

Cinders     

800 

700 

600 

500 

400 

NOTE. — For  variations  in  the  moduli  of  elasticity  see  section  on  "Working  Stresses." 

Bearing.  When  compression  is  applied  to  a  surface  of  concrete  of  at  least  twice 
the  loaded  area,  a  stress  of  35  per  cent  of  the  compressive  strength  may  be  allowed 
in  the  area  actually  under  load. 

t  See  Consistency,  page  191 
*See  foot  note,  page  191. 

209 


CORRUGATED      BAR      COMPANY,     INC. 


Axial  Compression.  For  concentric  compression  on  a  plain  concrete  pier, 
the  length  of  which  does  not  exceed  four  diameters,  or  on  a  column  reinforced  with 
longitudinal  bars  only,  the  length  of  which  does  not  exceed  12  diameters,  22.5  per 
cent  of  the  compressive  strength  may  be  allowed. 

For  other  forms  of  columns  the  stresses  obtained  from  the  ratios  given  in  the  pre- 
ceding section  on  "Design"  may  govern. 

Compression  in  Extreme  Fiber.  The  extreme  fiber  stress  of  a  beam,  calculated 
on  the  assumption  of  a  constant  modulus  of  elasticity  for  concrete  under  working 
stresses  may  be  allowed  to  reach  32.5  per  cent  of  the  compressive  strength.  Adjacent 
to  the  support  of  continuous  beams  stresses  15  per  cent  higher  may  be  used. 

Shear  and  Diagonal  Tension.  In  calculations  on  beams  in  which  the  maximum 
shearing  stress  in  a  section  is  used  as  the  means  of  measuring  the  resistance  to  diagonal 
tension  stress,  the  following  allowable  values  for  the  maximum  vertical  shearing  stress 
in  concrete,  calculated  by  the  method  given  in  Formula  22  (see  page  8)  are  recom- 
mended : 

(a) — For  beams  with  horizontal  bars  only  and  without  web  reinforcement,  2  per 
cent  of  the  compressive  strength. 

(6) — For  beams  with  web  reinforcement  consisting  of  vertical  stirrups  looped  about 
the  longitudinal  reinforcing  bars  in  the  tension  side  of  the  beam  and  spaced  hori- 
zontally not  more  than  one-half  the  depth  of  the  beam;  or  for  beams  in  which  longi- 
tudinal bars  are  bent  up  at  an  angle  of  not  more  than  45  degrees  or  less  than  20  degrees 
with  the  axis  of  the  beam,  and  the  points  of  bending  are  spaced  horizontally  not  more 
than  three-quarters  of  the  depth  of  the  beam  apart,  not  to  exceed  4^  per  cent  of  the 
compressive  strength. 

(c) — For  a  combination  of  bent  bars  and  vertical  stirrups  looped  about  the  rein- 
forcing bars  in  the  tension  side  of  the  beam  and  spaced  horizontally  not  more  than 
one-half  of  the  depth  of  the  beam,  5  per  cent  of  the  compressive  strength. 

(d) — For  beams  with  web  reinforcement  (either  vertical  or  inclined)  securely  at- 
tached to  the  longitudinal  bars  in  the  tension  side  of  the  beam  in  such  a  way  as  to 
prevent  slipping  of  bar  past  the  stirrup,  and  spaced  horizontally  not  more  than  one- 
half  of  the  depth  of  the  beam  in  case  of  vertical  stirrups  and  not  more  than  three- 
fourths  of  the  depth  of  the  beam  in  the  case  of  inclined  members,  either  with  longi- 
tudinal bars  bent  up  or  not,  6  per  cent  of  the  compressive  strength. 

The  web  reinforcement  in  case  any  is  used  should  be  proportioned  by  using  two- 
thirds  of  the  external  vertical  shear  in  Formula  24  or  25  (see  page  9).  The  effect  of 
longitudinal  bars  bent  up  at  an  angle  of  from  20  to  45  degrees  with  the  axis  of  the 
beam  may  be  taken  at  sections  of  the  beam  in  which  the  bent  up  bars  contribute  to 
diagonal  tension  resistance  (see  "Diagonal  Tension  and  Shear,"  page  198)  as  reducing 
the  shearing  stresses  to  be  otherwise  provided  for.  The  amount  of  reduction  of  the 
shearing  stress  by  means  of  bent  up  bars  will  depend  upon  their  capacity,  but  in  no 
case  should  be  taken  as  greater  than  43^  per  cent  of  the  compressive  strength  of 
the  concrete  over  the  effective  cross-section  of  the  beam  (Formula  22).  The  limit  of 
tensile  stress  in  the  bent  up  portion  of  the  bar  calculated  by  Formula  25,  using  in  this 
formula  an  amount  of  total  shear  corresponding  to  the  reduction  in  shearing  stress 
assumed  for  the  bent  up  bars,  may  be  taken  as  specified  for  the  working  stress  of 
Steel,  but  in  the  calculations  the  stress  in  the  bar  due  to  its  part  as  longitudinal 

210 


USEFUL,      DATA 


reinforcement  of  the  beam  should  be  considered.  The  stresses  in  stirrups  and  inclined 
members  when  combined  with  bent  up  bars  are  to  be  determined  by  finding  the  amount 
of  the  total  shear  which  may  be  allowed  by  reason  of  the  bent  up  bars,  and  subtracting 
this  shear  from  the  total  external  vertical  shear.  Two-thirds  of  the  remainder  will  be 
the  shear  to  be  carried  by  the  stirrups,  using  Formulas  24  or  25  (see  page  9). 

Where  punching  shear  occurs,  provided  the  diagonal  tension  requirements  are  met, 
a  shearing  stress  of  6  per  cent  of  the  compressive  strength  may  be  allowed. 

Bond.  The  bond  stress  between  concrete  and  plain  reinforcing  bars  may  be 
assumed  at  4  per  cent  of  the  compressive  strength,  or  2  per  cent  in  the  case  of  drawn 
wire.  In  the  best  types  of  deformed  bar  the  bond  stress  may  be  increased,  but  not  to 
exceed  5  per  cent  of  the  compressive  strength  of  the  concrete. 

Reinforcement.  The  tensile  or  compressive  stress  in  steel  should  not  exceed 
16,000  pounds  per  square  inch. 

In  structural  steel  members  the  working  stresses  adopted  by  the  American  Railway 
Engineering  Association  are  recommended. 

Modulus  of  Elasticity.  The  value  of  the  modulus  of  elasticity  of  concrete  has 
a  wide  range,  depending  on  the  materials  used,  the  age,  the  range  of  stresses  between 
which  it  is  considered,  as  well  as  other  conditions.  It  is  recommended  that  in  compu- 
tations for  the  position  of  the  neutral  axis,  and  for  the  resisting  moment  of  beams 
and  for  compression  of  concrete  in  columns,  it  be  assumed  as : 

(a) — One-fortieth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  not 
more  than  800  pounds  per  square  inch. 

(6) — One-fifteenth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  greater 
than  800  pounds  per  square  inch. 

(c) — One-twelfth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  greater 
than  2,200  pounds  per  square  inch,  and  less  than  2,900  pounds  per  square  inch,  and 

(d) — One-tenth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  greater 
than  2,900  pounds  per  square  inch. 

Although  not  rigorously  accurate,  these  assumptions  will  give  safe  results.  For  the 
deflection  of  beams  which  are  free  to  move  longitudinally  at  the  supports,  in  using 
formulas  for  deflection  which  do  not  take  into  account  the  tensile  strength  developed 
in  the  concrete,  a  modulus  of  one-eighth  of  that  of  steel  is  recommended. 


211 


CORRUGATED   BAR   COMPANY,  INC. 


SUBJECT  INDEX 

PAGES 

AMERICAN  Society  for  Testing  Materials,  cement  specifications 186-187 

AREAS— Circles 182-183 

Circular  segments 174 

Column  sections 157-158 

Corrugated  Bars 164 

Reinforcement  for  slabs 148 

Triangles 175 

Various  sections 168-171 

Wire    ..;... 167 

BARS — Moments  of  inertia 160 

Reinforcing 164^166 

Specifications 188-189 

BEAMS — Continuous,  moments  and  shears 38-48 

Continuous,  moment  factors 196-197 

Quantities  of  concrete 161 

Rectangular,  designing  diagrams,  explanation 10 

Rectangular,  diagrams  for  values  of  j,  k  and  K 16 

Rectangular,  formulas 6 

Rectangular,  standard  notation 

Rectangular,  tables  of  safe  loads 79-90 

Rectangular,  table  of  values  of  p,  k,  j  and  K 

Reinforced  for  compression,  designing  diagrams,  explanation  .    .    .  12-13 

Reinforced  for  compression,  diagram 20 

Reinforced  for  compression,  formulas 8 

Reinforced  for  compression,  standard  notation 5 

Span  of 194-195 

Stirrup  reinforcement,  table 107 

Tee,  continuous,  explanation  of  tables 59-60 

Tee,  designing  diagrams,  explanation 

Tee,  diagrams  for  values  of  K  and  j 17-18 

Tee,  diagrams  for  values  of  k  and  j 

Tee,  dimensions 195 

Tee,  formulas 

Tee,  standard  notation 5 

Tee,  tables  of  safe  loads 91-106 

Wooden 173 

BENDING  and  direct  stress,  combined 13-14 

and  direct  stress,  combined,  diagrams 21-24 

BOND — Formulas 

Standard  notation 6 

Strength 197-198 

BRACKETS 194-195 

BUILDING  code  requirements  for  live  loads 51-52 

BUILDING  materials — weights  of 56 

CAPS  for  reinforced  concrete  piles 141-142 

CEMENT  specifications 186-187 

CIRCLES — Areas  and  circumferences 182-183 

CIRCULAR  segments — Areas 

CIRCUMFERENCES  of  circles 182-183 

COLUMN — Heads,  diagram  for  volume  of  concrete  in 

Sections,  areas,  perimeters,  etc 157-158 

Spirals,  pitch  and  percentage 150 

Spirals,  standard  wire  and  spacers 156 

Spirals,  weight  per  foot 151-155 

Verticals,  moments  of  inertia 159-160 

212 


USEFUL      DATA 


PAGES 

COLUMNS — Bending  moments 209 

Designing  diagrams,  explanation 13-14 

Formulas 

Joint  Committee  recommendations 200-202 

Length 195 

Spiral,  tables  of  safe  loads 122-132 

Square  tied,  tables  of  safe  loads 115-121 

Standard  notation 6 

Tables,  explanation 

Vertical  steel  for  various  percentages  of  core  area 149 

Wooden 173 

COMPRESSIVE  reinforcement  of  beams,  diagram 20 

CONCRETE — General  specifications 190-193 

Massive ,    .  194 

Quantities  of  materials 163 

CONSTRUCTION — General  specifications 190-193 

Recommendations  on  design  and  working  stresses,  Joint 

Committee 194-211 

CoRR-Plate  floors— Explanation 108-109 

Tables 110-113 

CORRUGATED  Bars 164 

CUBES  and  cube  roots  of  numbers 182-183 

DECIMALS  of  a  foot 185 

of  an  inch 184 

DEFLECTION — General  formulas 26-37 

DESIGN — Final  report  of  Joint  Committee 194-211 

DESIGNING  diagrams — Explanation 10-14 

DIAGRAM — Compressive  reinforcement  of  beams 20 

Distribution  of  load  for  rectangular  slabs 25 

Values  of  K,  j  and  k  for  rectangular  beams  and  slabs 16 

Values  of  k  and  j  for  tee  beams 19 

Values  of  K'  for  combined  bending  and  direct  stress 21 

Values  of  k  for  combined  bending  and  direct  stress 22 

Volume  of  concrete  in  column  heads 162 

DIAGRAMS — Designing,  explanation 10-14 

Moment  and  shear  coefficients  for  continuous  beams,  equal  spans  45-48 

Values  of  F  for  combined  bending  and  direct  stress 23-24 

Values  of  K  and  j  for  tee  beams 17-18 

DIAGONAL  tension  and  shear 198-200 

DISTRIBUTION  of  load  for  rectangular  slabs,  diagram 25 

EARTH  pressures 144 

F — Diagram  for  values  of,  for  combined  bending  and  direct  stress    ....  23-24 

FIREPROOFING — Explanation  of  slab  and  beam  tables 58 

FLAT  SLAB— Explanation  of 108-109 

Column  heads,  diagram  for  volume  of  concrete  in 162 

Joint  Committee  recommendations 202-209 

Floors,  tables 110-113 

FLOORS  and  roofs — Explanation  of  tables 57-60 

FOOTINGS — Combined  column,  tables 136-139 

Explanation  of  tables 133-135 

For  reinforced  concrete  piles • 141-142 

Square  column,  table 140 

FORMULAS — For  columns 

For  properties  of  sections 168-171 

For  reactions,  bending  moments,  shears  and  deflections    ...  26-37 

For  reinforced  concrete  design 5-9 

For  trigonometric  solution  of  triangles 175 

213 


CORRUGATED      BAR      COMPANY,     INC. 


PAGES 

FOUNDATIONS — Bearing  capacity  of  soils 147 

FRACTIONS  and  equivalent  decimals 184 

FRICTION — Coefficients  and  angles 147 

FUNCTIONS — Natural  trigonometric 176-181 

of  numbers 182-183 

GYRATION — Radius  of,  various  sections 168-171 

INERTIA — Moments  of,  bars 166 

Moments  of,  column  sections 157-158 

Moments  of,  column  verticals 159 

Moments  of,  various  sections 168-171 

j — Diagram  for  values  in  rectangular  beams  and  slabs 16 

j — Diagram  for  values  in  tee  beams 17-19 

j — Table  of  values  for  rectangular  beams  and  slabs 15 

JOINT  Committee — Final  report  on  design  and  working  stresses 194-211 

K — Diagram  for  values  of,  rectangular  beams  and  slabs 16 

Diagram  for  values  of,  tee  beams. 17-18 

Table  of  values,  rectangular  beams  and  slabs 15 

k — Diagram  for  values  of,  combined  bending  and  direct  stress 22 

Diagram  for  values  of,  rectangular  beams 16 

Diagram  for  values  of,  tee  beams 19 

Table  of  values  of,  rectangular  beams  and  slabs 15 

K' — Diagram  for  values  of,  combined  bending  and  direct  stress 21 

LOAD — Building  code  requirements „ 51-52 

Distribution  of,  for  rectangular  slabs 25 

LOADS — Dead  and  live 194 

Safe,  for  flat  slab  floors 110-113 

Safe,  for  rectangular  beams 79-90 

Safe,  for  spiral  columns 122-132 

Safe,  for  square  tied  columns 115-121 

Safe,  superimposed  for  clay  tile  ribbed  slabs 67-72 

Safe,  superimposed  for  ribbed  slabs 73-78 

Safe,  superimposed  for  solid  concrete  slabs 61-66 

Safe,  for  tee  beams 91-106 

In  warehouses 49-50 

For  wooden  beams  and  columns 173 

LOGARITHMS  of  numbers 182-183 

MANUFACTURERS'  standard  specifications  for  deformed  bars 188-189 

MATERIALS — Building,  weight  of 

Quantities  for  concrete 163 

Weights  of 53-55 

MODULUS — Section,  various  sections 168-171 

MOMENTS — Bending,  continuous  beams 38-48 

Bending,  general  formulas  for 28-37 

Of  inertia,  bars .160 

Of  inertia,  column  sections 157-158 

Of  inertia,  column  verticals 159 

Of  inertia,  various  sections 168-171 

Theorem  of  three 38-44 

p — Table  of  values  of,  rectangular  beams  and  slabs 

PERIMETERS — Column  sections 157-158 

PILE  caps • 141-142 

PILES — Reinforced  concrete 143 

PRESSURES — Earth  and  water 144 

PROPERTIES  of  sections 168-171 

RADIUS  of  gyration  of  various  sections 168-171 

REACTIONS — General  formulas  for 28-37 

RECIPROCALS  of  numbers 182-183 

214 


USEFUL      DATA 


PAGES 

REINFORCEMENT — Corrugated  Bars 164-166 

RETAINING  walls — Cantilever 145-146 

RIBBED  slabs— Clay  tile,  safe  load  tables 67-72 

Explanation  of  tables  for 59 

Steel  or  wood  forms,  safe  load  tables 73-78 

ROOFS — Floors  and,  explanation  of  tables 57-60 

SECTION  modulus — Various  sections 168-171 

SECTIONS— Properties  of 168-171 

SEGMENTS — Area  of  circular 174 

SHEAR  for  continuous  beams 38-48 

SHEAR — Diagonal  tension  and 198-200 

Explanation  of  slab  and  beam  tables 58 

Formulas  for 

General  formula  for 28-37 

Standard  notation  for 6 

SHRINKAGE — Reinforcing  for 202 

SLAB — Area  of  reinforcement  per  foot  width 148 

Flat,  Joint  Committee  recommendation 202-209 

SLABS — Clay  tile  ribbed,  explanation  of  tables 59 

Clay  tile  ribbed,  tables  of  safe  loads 67-72 

Continuous,  moment  factors 196-197 

Distribution  of  load  for  rectangular 25 

Flat,  explanation  of 108-109 

Flat,  tables 110-113 

Ribbed,  explanation  of  tables 59 

Ribbed,  table  of  safe  loads 73-78 

Solid  concrete,  explanation  of  tables 58-59 

Solid  concrete,  tables  of  safe  loads 61-66 

Supported  on  four  sides 

SOIL  values — Combined  column  footings 136-139 

Square  column  footings 

SOILS — Bearing  capacity  of 

SPACERS — Column  spiral,  tee  section 

SPACING  of  slab  bars  for  steel  areas  per  foot  width 148 

SPAN  of  beams 194-195 

SPECIFICATIONS  for  deformed  bars 188-189 

for  Portland  cement 186-187 

general,  for  reinforced  concrete 190-193 

SPIRALS — Column,  pitch  and  percentage 

Column,  standard  wire  and  spacers 

Column,  weight  per  foot  height 151-155 

SQUARES  and  square  roots  of  numbers 182-183 

STIRRUP  reinforcement  for  uniformly  loaded  beams 107 

STRESS — Combined  bending  and  direct 

Combined  bending  and  direct,  diagrams 21-24 

STRESSES — Joint  Committee  recommendations 194-211 

Temperature  and  shrinkage 202 

Timber 172 

Working,  Joint  Committee 209-211 

TABLES — American  Steel  and  Wire  Company's  gauges 

Area  of  reinforcement  per  foot  width  of  slab 

Areas  of  circular  segments 

Bearing  capacity  of  soils 

Caps  for  reinforced  concrete  piles 141-142 

Cantilever  retaining  walls 145-146 

Column  spiral  weights 151-155 

Column  vertical  steel 149 

215 


CORRUGATED   BAR   COMPANY,  INC. 


TABLES — Combined  column  footings 136-139 

Corrugated  Bars 164 

Decimals  of  a  foot 185 

Decimals  of  an  inch 184 

Earth  and  water  pressures 144 

Flat  slab  floors 110-113 

Functions  of  numbers 182-183 

Moments  of  inertia  of  bars 160 

Moments  of  inertia  of  column  verticals 159 

Natural  trigonometric  functions 176-181 

Properties  of  column  sections 157-158 

Properties  of  sections 168-171 

Quantities  of  materials  for  concrete 163 

Reinforced  concrete  piles 143 

Safe  loads,  clay  tile  ribbed  slabs 67-72 

Safe  loads,  rectangular  beams 79-90 

Safe  loads,  ribbed  slabs,  steel  or  wood  forms 73-78 

Safe  loads,  solid  concrete  slabs 61-66 

Safe  loads,  tee  beams 91-106 

Spiral  columns,  safe  loads 122-132 

Spiral  wire  and  spacers 156 

Spirals,  pitch  and  percentage 150 

Square  column  footings 140 

Square  tied  columns,  safe  loads 115-121 

Stirrup  reinforcement  for  uniformly  loaded  beams 107 

Timber 172-173 

Trigonometric  solution  of  triangles 175 

Values  of  p,  k,  j  and  K 15 

Volume  of  concrete  in  beams 161 

TEMPERATURE — Reinforcing  for 202 

THEOREM  of  three  moments 38-44 

TIMBER— Tables 172-173 

TRIANGLES — Trigonometric  solution  of 175 

TRIGONOMETRIC — Natural,  functions 176-181 

Solution  of  triangles 

VOLUMES — Column  sections 157-158 

Of  concrete  in  beams 161 

Of  concrete  in  column  heads 162 

WALLS — Cantilever  retaining 145-146 

WAREHOUSES — Table  of  weight  of  contents 49-50 

WATER  pressure 144 

WEB  reinforcement — Formulas  for 8-9 

Standard  notation  for 

For  uniformly  loaded  beams 107 

WEIGHTS  of  building  materials 56 

Column  sections 157-158 

Column  spirals 151-155 

Corrugated  Bars 164 

Of  materials 53-55 

Of  timber 172 

WIRE — American  Steel  and  Wire  Company's  gauges 167 

Column  spiral 

WOODEN  beams  and  columns    ,               173 


216 


RICE  LEADERS  OF  THE  WORLD  ASSOCIATION 

ANNOUNCES  THE  ELECTION  To 
MEMBERSHIP  OF  THE 

CORRUGATED  BAR  COMPANY,  INC. 


8Y  INVITATION 
MEMBER  OF 


NEW  YORK.  U.S. A. 


THIS  Association  is  a  cooperative  organization  composed  solely  of 
concerns  which  adhere  to  the  highest  standards  in  the  conduct 
of  their  business.  These  are  the 

QUALIFICATIONS  FOR  MEMBERSHIP 

HONOR:          A  recognized  reputation  for  fair  and  honorable 
business  dealings. 

QUALITY:       An  honest  product,  of  quality  truthfully  repre- 
sented. 

STRENGTH  :     A  responsible  and  substantial  financial  standing. 

SERVICE:        A  recognized  reputation  for  conducting  business 
in  prompt  and  efficient  manner. 

Membership  in  the  Association  is  an  evidence  of  the  distinctive 
position  which  the  Corrugated  Bar  Company,  Inc.  holds  as  a  Specialist 
in  Concrete  Reinforcement  and  Design. 

It  testifies  as  to  the  quality  of  this  company's  products  and  ser- 
vice, and  the  character  of  the  directing  officials. 

It  is  a  further  assurance  that  these  products  are  made  by  a  con- 
cern worthy  of  utmost  confidence,  as  only  manufacturers  of  the 
highest  standing  in  name,  product  and  policy  are  privileged  to  display 
the  Association  Emblem. 


CORRUGATED  BARS 

THE  question  of  using  plain  or  deformed  bars  for  reinforced  concrete  construction 
has  been  answered  in  the  United  States  where  the  volume  of  such  construction 
is  probably  greater  than  in  all  the  rest  of  the  world.  Fifteen  years  ago  about  80% 
of  the  reinforcement  used  was  plain  bars,  to-day  80%  is  deformed  bars. 

Nearly  all  building  codes,  architects'  and  engineers'  specifications  and  committee 
recommendations  of  technical  societies  allow  larger  working  values  for  the  bond  stress 
of  deformed  than  for  plain  bars. 

A  review  of  available  test  data  on  bond  shows  clearly  that  American  practice  is  on 
a  very  sound  basis.  Diagram  1  is  the  average  resulting  from  the  tabulation  and 

analysis  of  the  thousands  of  bond  tests 
made  by  recognized  authorities  in  the 
United  States  and  Europe  on  both  plain 

CORRUGATED  ROUNDS  and  Corrugated  Bars.    The  variation  in 

the  case  of  plain  bars,  from  a  very  low 

value  for  a  minimum  to  a  maximum  value  which  approximates  only  the  average  of 
Corrugated  Bars,  is  due  entirely  to  the  fact  that  the  bond  of  a  plain  bar  is  a  function 
of  accidental  surface  condition.  A  smooth  bar  has  a  very  low  bond  value;  a  rusty, 
pitted,  rough  bar  may  have  a  high  value. 

An  important  difference  in  behavior  between  plain  and  Corrugated  Bars  is  shown  in 
Diagram  2.  This  diagram  is  a  composite  of  load  slip  curves  taken  from  University  of 
Illinois  tests  where  conditions  were  practically  identical,  and  illustrates  clearly  that 
plain  bars  reach  a  maximum  bond  value  at  about  0.01  inch  slip  and  then  decrease  while 
Corrugated  Bars  have  much  higher  bond  at  the  same  slip  and  increase  in  resistance 
until  a  final  value  several  times  that  of  plain  bars  is  reached. 

It  is  not  good  engineering  practice  to  leave  the  bond — the  most  important  function 
of  the  reinforcement — to  chance,  while  all  the  other  physical  properties  of  the  material 
are  required  to  conform  to  rigid  specifi- 
cations within  narrow  limits. 

To  realize   the   highest    efficiency    of 

bond  value,  a  deformed   bar  of  proper  CORRUGATED  SQUARES 

design  is  required;  merely  roughening  the 

surface  of  a  bar  by  haphazard  projections  may  actually  decrease  its  bond  value.  The 
twisted  bar,  for  example,  for  years  considered  a  standard  deformed  bar,  has  been  found 
on  careful  examination  to  have  lower  bond  resistance  than  a  plain  bar. 

The  conditions  governing  the  design  of  a  satisfactory  deformed  bar  are  clearly  stated 
in  Bulletin  No.  71,  University  of  Illinois,  Engineering  Experiment  Station,  as  follows: 
"In  a  deformed  bar  of  good  design  the  projections  should  present  bearing  faces  as 
nearly  as  possible  at  right  angles  to  the  axis  of  the  bar.  The  areas  of  the  projections 
should  be  such  as  to  preserve  the  proper  ratio  between  the  bearing  stress  against  the 
concrete  ahead  of  the  projections  and  the  shearing  stress  over  the  surrounding  en- 
velope." 

Of  all  the  deformed  bars  on  the  market  the  Corrugated  Bar  is  the  only  one  that 
substantially  fulfills  these  requirements. 


1100 


1000 


100 


1100 


1000 


Summary-for 
Beam  Tests 


Summary  for 
Pull  Out  Tests 


Note:-;  Tests  included  cover 
plain,  bars-from 
"  to  IY«H  diam. 
and  Corrugated  Bars 
from.  V*n  to  \  Yx  diam. 
All  embedments  8? 
Age  60  to  70  days 
Mixrl:-2:4. 


Key  to  Diagram 
Minimum  Value 
Average  Value 
Maximum.  Value 


100 


DIAGRAM  1 


0  01         ..02          .03          .04         .05 

Slip  m.inches 

DIAGRAM  2 


CORR-MESH 

CORR-MESH  is  a  ribbed  expanded  metal — a  one-piece  product,  made 
from  a  high-grade  of  rolled  sheet  steel.  The  ribs  provide  strength 
and  stiffness  to  the  sheets  which  give  firm  support  to  concrete  and 
plaster  both  during  construction  and  after.    The  metal  between  the 
ribs  is  expanded  into  a  diamond  mesh. 


!*3>Vcenter  to  center  of  ribs-*i 
•13" center  to  center  of  outside  ribs- 


%*  RIB  CORR-MESH 

For  walls  and  partitions,  %"  Rib  Corr-Mesh  is  plastered  both  sides 
with  cement  mortar,  forming  a  monolithic  wall  of  great  strength.  The 
ribs  do  away  with  extra  studding — a  saving  in  material  and  labor  cost. 

For  walls  and  floors,  J4"  Rib  Corr-Mesh  acts  as  form  work.  It 
supports  the  wet  concrete;  no  deck  centering  is  required. 

APPLICATION  OF  %"  RIB  CORR-MESH 

FOUNDRIES  AND  LIGHT  MANUFACTURING  PLANTS:  Replaces  cor- 
rugated iron  and  wood  siding.  Corr-Mesh  is  the  ideal  method  of  con- 
struction for  roofs,  floors,  partitions  and  exterior  walls. 

RAILROADS:  Handsome,  permanent,  fireproof  stations,  sheds  and 
wayside  buildings  in  stucco  at  low  cost. 

AMUSEMENT  PARK  BUILDINGS  :  Corr-Mesh  makes  possible  the  only 
low  cost  construction  on  which  insurance  can  be  obtained. 


CORR-MESH 


CENTER  TO  CENTER  OF  RIBS 


18    CENTER  TO  CENTER  OF  OUTSIDE  RIBS 


%6"  RIB  CORR-MESH 

For  ceilings,  5/ie"  Rib  Corr-Mesh  is  used  extensively,  where  it 
greatly  reduces  the  material  required  in  the  supporting  framework, 
and  cuts  down  the  cost  of  erection. 

For  stucco  construction  it  eliminates  furring  strips  and  makes  a 
strong  and  permanent  reinforcement  for  the  plaster  covering. 

APPLICATION  OF  5/io"  RIB  CORR-MESH 

RESIDENCES:  Stucco  walls  are  handsome,  permanent  and  fire- 
resisting.  Old  wooden  houses  may  be  transformed  at  small  cost  into 
attractive  residences  of  greatly  increased  value. 

GARAGES,  STABLES  AND  OUTBUILDINGS  of  stucco  construction  with 
6/io"  Rib  Corr-Mesh  are  low  in  cost,  permanent,  and  free  from  repair 
expense. 

FENCES  which  present  an  artistic  and  substantial  appearance  are 
constructed  with  Corr-Mesh. 


CORRUGATED  BAR   COMPANY,  INC. 

BUFFALO,  N.  Y. 


FABRICATED  REINFORCEMENT  READY  TO 
PLACE  IN  THE  FORMS 


READY  TO  PLACE 

CORK-BAR  UNITS 


SHOP  fabricated  reinforcement  marks  a  turning  point 
in  reinforced  concrete  construction.  It  is  only  a 
question  of  time  when  the  practice  of  organizing  a  fab- 
rication crew,  for  each  job,  with  local  inexperienced 
common  labor,  must  give  way  to  well-established  shop 
practice,  in  which  hand  labor  is  replaced  by  machine 
production. 

Shop  fabrication  secures  accuracy,  thereby  eliminat- 
ing one  important  factor  of  uncertainty  in  construc- 
tion.   It  secures  economy  and  facilitates  supervision 
and  inspection.    It  saves  storage  and  working  space 
at  the  building  site,  often  a  matter  of  great  importance, 
and  by  decreasing  the  amount  of  labor  in  the  field  removes  some  of 
the  uncertainty  and  annoyance  connected  with  the  handling  of  labor. 
Reinforcement  should  not  only  be  fabricated  in  the  shop,  but 
assembled  into  units,  as  far  as  practicable,  properly  marked  and  made 
ready  to  place  directly  in  the  forms. 

For  beam  reinforcement  the  Corr-Bar  Unit  is  an  ideal  example  of 
shop  fabricated  reinforcement.  Instead  of  depending  upon  the  skill 
of  the  individual  workman  to  fabricate  and  assemble  twenty  to 
thirty  pieces  and  place  them  properly  in  the  forms,  one  unit  is  made 
in  the  shop  by  machine  operators  under  the  direction  of  an  organi- 
zation especially  trained  to  do  this  work.  The  unit  is  inspected  and 
marked  and  so  equipped  with  supporting  devices  as  to  insure  its 
proper  place  in  the  structure. 


CIVI 


ENGINEERING  SERVICE  DEPARTMENT 


THE  Corrugated  Bar  Company,  Inc.,  since  its  inception,  more  than 
twenty-five  years  ago,  has  been  primarily  an  engineering  organiza- 
tion. It  has  been  a  pioneer  in  the  field  of  reinforced  concrete  not 
only  in  the  development  of  scientifically  correct  reinforcing  materials 
and  systems  of  construction,  but  through  investigation  and  presenta- 
tion of  rational  methods  of  design. 

Under  the  direction  of  its  engineers  elaborate  and  painstaking 
research  and  test  programs  have  been  carried  out,  earning  for  the 
company  an  enviable  reputation  and  standing  in  professional  circles. 

The  engineering  department  has  developed  under  highly  competi- 
tive conditions,  making  it  of  necessity  efficient  and  economical  in  the 
execution  of  its  designs  and  it  is  safe  to  say  that  for  variety  and 
wealth  of  experience  it  is  unsurpassed  by  any  organization  of  its 
kind.  As  a  result  of  its  experience  it  has  been  called  upon  frequently 
to  act  in  a  consulting  capacity  on  numerous  reinforced  concrete 
structures  in  the  United  States  and  many  foreign  countries.  The 
constantly  increasing  demand  for  this  class  of  service  resulted  in 
the  organization  of  an  Engineering  Service  Department. 

The  service  rendered  by  this  department — divorced  entirely  from 
the  company's  products — is  available  to  architects  and  engineers  on 
a  fee  basis  and  consists  of: 

1.  A  study  of  conditions  and  selection  of  a  type  of  construction  best  suited  to  the 
purpose  of  the  building. 

2.  Preliminary  and  comparative  sketches,  estimates  and  cost  data  as  a  basis  of 
negotiation  between  the  architect  or  engineer  and  his  client. 

3.  Preparation  of  detail  plans  and  specifications  including  placing  diagrams,  fab- 
rication details  and  bar  lists. 

By  the  use  of  this  Service  the  owner  obtains  a  low  bid  on  the  con- 
struction best  suited  to  his  building  and  it  guarantees  full  patent  pro- 
tection on  any  materials  or  construction  involved  in  the  plans  supplied. 


CORRUGATED  BAR  COMPANY,  INC. 

MUTUAL  LIFE  BUILDING 
BUFFALO,  N.  Y. 

DISTRICT  OFFICES 

NEW  YORK,  N.  Y. 
Whitehall  Building,  17  Battery  Place 

CHICAGO,  ILL. 
Great  Northern  Building,  20  W.  Jackson  Street 

PHILADELPHIA,  PA. 
Transportation  Building,  26  S.  Fifteenth  Street 

BOSTON,  MASS. 

27  School  Street 

ST.  Louis,  Mo. 

Boatmen's  Bank  Building 

DETROIT,  MICH. 
Penobscot  Building 

MILWAUKEE,  Wis. 
Wells  Building 

KANSAS  CITY,  Mo. 
Waldheim  Building 

ST.  PAUL,  MINN. 
Pioneer  Building 

ATLANTA,  GA. 
Grant  Building 

SYRACUSE,  N.  Y. 
Union  Building 

HOUSTON,  TEXAS 
700  N.  San  Jacinto  Street 


MUTTHEWS-NORTHRL'P 


CALIFORNIA 

PARTMENT  OF  CIVIL  ENQ!NSi£ 
.  CALR  OK 


UNIVERSITY  OF  CALIFORNIA 
OF  CIVIL  ENGINES, 
Zi  -^»>iiA 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 


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